Journal articles: 'Confidence dispersion'

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Chen, Cong, and Robert W. Tipping. "Confidence Interval of a Proportion with Over-dispersion." Biometrical Journal 44, no. 7 (October 2002): 877–86. http://dx.doi.org/10.1002/1521-4036(200210)44:7<877::aid-bimj877>3.0.co;2-7.

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Geedipally, Srinivas Reddy, and Dominique Lord. "Effects of Varying Dispersion Parameter of Poisson–Gamma Models on Estimation of Confidence Intervals of Crash Prediction Models." Transportation Research Record: Journal of the Transportation Research Board 2061, no. 1 (January 2008): 46–54. http://dx.doi.org/10.3141/2061-06.

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In estimating safety performance, the most common probabilistic structures of the popular statistical models used by transportation safety analysts for modeling motor vehicle crashes are the traditional Poisson and Poisson–gamma (or negative binomial) distributions. Because crash data often exhibit overdispersion, Poisson–gamma models are usually the preferred model. The dispersion parameter of Poisson–gamma models had been assumed to be fixed, but recent research in highway safety has shown that the parameter can potentially be dependent on the covari-ates, especially for flow-only models. Given that the dispersion parameter is a key variable for computing confidence intervals, there is reason to believe that a varying dispersion parameter could affect the computation of confidence intervals compared with confidence intervals produced from Poisson–gamma models with a fixed dispersion parameter. This study evaluates whether the varying dispersion parameter affects the computation of the confidence intervals for the gamma mean (m) and predicted response (y) on sites that have not been used for estimating the predictive model. To accomplish that objective, predictive models with fixed and varying dispersion parameters were estimated by using data collected in California at 537 three-leg rural unsignalized intersections. The study shows that models developed with a varying dispersion parameter greatly influence the confidence intervals of the gamma mean and predictive response. More specifically, models with a varying dispersion parameter usually produce smaller confidence intervals, and hence more precise estimates, than models with a fixed dispersion parameter, both for the gamma mean and for the predicted response. Therefore, it is recommended to develop models with a varying dispersion whenever possible, especially if they are used for screening purposes.

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Gao, Jie, Xin-Kang Wang, and Hui Chen. "The Relationship Between P-Wave Dispersion, QTc Dispersion, and Gestational Hypertension." American Journal of Hypertension 35, no. 2 (February 1, 2022): 207. http://dx.doi.org/10.1093/ajh/hpab118.

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Abstract Background To analyze the relationship between gestational hypertension and P-wave dispersion and QTc interval dispersion. Methods From January 2017 to December 2019, 213 pregnant women who met the diagnosis of hypertension were selected as gestational hypertension with 248 healthy pregnant women as controls. The basic data, P-wave dispersion, and QTc dispersion were compared between the 2 groups, and binary logistic regression analysis was performed. Results The minimum time of P wave (78.59 ± 9.32 vs. 94.61 ± 7.03 ms) and the minimum time of QTc (384.65 ± 21.69 vs. 401.91 ± 15.49 ms) in gestational hypertension were significantly lower than those in the controls. The dispersion of P wave (42.75 ± 9.94 vs. 14.91 ± 4.03 ms), QTc (57.15 ± 16.10 vs. 21.42 ± 6.07 ms), the maximum time of P wave (121.34 ± 7.22 vs. 112.53 ± 6.43 ms), and the maximum time of QTc (441.80 ± 25.42 vs. 429.74 ± 27.83 ms) in gestational hypertension were significantly higher than those in the controls (all P < 0.05). Logistic regression analysis showed that P-wave dispersion (odds ratio = 1.795, 95% confidence interval 1.266–2.546), QTc minimum time (odds ratio = 0.905, 95% confidence interval 0.833–0.983), and QTc dispersion (odds ratio = 1.216, 95% confidence interval 1.042–1.420) were correlated with gestational hypertension. Conclusions P-wave dispersion and QTc dispersion are associated with gestational hypertension.

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Chen, Xue-Dong, Nian-Sheng Tang, and Xue-Ren Wang. "On confidence regions of semiparametric nonlinear reproductive dispersion models." Statistics 43, no. 6 (December 2009): 583–95. http://dx.doi.org/10.1080/02331880802689332.

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Yosboonruang, Noppadon, Sa-Aat Niwitpong, and Suparat Niwitpong. "Simultaneous confidence intervals for all pairwise differences between the coefficients of variation of rainfall series in Thailand." PeerJ 9 (June 23, 2021): e11651. http://dx.doi.org/10.7717/peerj.11651.

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The delta-lognormal distribution is a combination of binomial and lognormal distributions, and so rainfall series that include zero and positive values conform to this distribution. The coefficient of variation is a good tool for measuring the dispersion of rainfall. Statistical estimation can be used not only to illustrate the dispersion of rainfall but also to describe the differences between rainfall dispersions from several areas simultaneously. Therefore, the purpose of this study is to construct simultaneous confidence intervals for all pairwise differences between the coefficients of variation of delta-lognormal distributions using three methods: fiducial generalized confidence interval, Bayesian, and the method of variance estimates recovery. Their performances were gauged by measuring their coverage probabilities together with their expected lengths via Monte Carlo simulation. The results indicate that the Bayesian credible interval using the Jeffreys’ rule prior outperformed the others in virtually all cases. Rainfall series from five regions in Thailand were used to demonstrate the efficacies of the proposed methods.

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Thangjai, Warisa, Sa-Aat Niwitpong, and Suparat Niwitpong. "Bayesian Confidence Intervals for Coefficients of Variation of PM10 Dispersion." Emerging Science Journal 5, no. 2 (April 1, 2021): 139–54. http://dx.doi.org/10.28991/esj-2021-01264.

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Herein, we propose the Bayesian approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. For the first case, the Bayesian approach was compared with large-sample, Chi-squared, and approximate fiducial approaches via Monte Carlo simulation. For the second case, the Bayesian approach was compared with the method of variance estimates recovery (MOVER), modified MOVER, and approximate fiducial approaches using Monte Carlo simulation. The results show that the Bayesian approach provided the best approach for constructing the confidence intervals for both the coefficient of variation of a log-normal distribution and the difference between the coefficients of variation of two log-normal distributions. To illustrate the performances of the confidence limit construction approaches with real data, they were applied to analyze real PM10 datasets from the Nan and Chiang Mai provinces in Thailand, the results of which are in agreement with the simulation results. Doi: 10.28991/esj-2021-01264 Full Text: PDF

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Bonett, Douglas G., and Edith Seier. "Confidence Interval for a Coefficient of Dispersion in Nonnormal Distributions." Biometrical Journal 48, no. 1 (February 2006): 144–48. http://dx.doi.org/10.1002/bimj.200410148.

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Pobedin, A. V., A. A. Dolotov, and A. I. Iskaliev. "Estimated determination of noise dispersion of towing vehicles." Izvestiya MGTU MAMI 9, no. 2-1 (January 20, 2015): 119–22. http://dx.doi.org/10.17816/2074-0530-67265.

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The paper discusses issues related to the possibility of obtaining of the value of noise dispersion of towing vehicles by calculation. The authors obtained mathematical expressions to determine the dispersion of depending on confidence interval of individual noise sources. The article shows a general procedure for evaluating of probable dispersion of the results of the estimated noise of a vehicle.

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Shilane, David, and Derek Bean. "Growth Estimators and Confidence Intervals for the Mean of Negative Binomial Random Variables with Unknown Dispersion." Journal of Probability and Statistics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/602940.

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The negative binomial distribution becomes highly skewed under extreme dispersion. Even at moderately large sample sizes, the sample mean exhibits a heavy right tail. The standard normal approximation often does not provide adequate inferences about the data's expected value in this setting. In previous work, we have examined alternative methods of generating confidence intervals for the expected value. These methods were based upon Gamma and Chi Square approximations or tail probability bounds such as Bernstein's inequality. We now propose growth estimators of the negative binomial mean. Under high dispersion, zero values are likely to be overrepresented in the data. A growth estimator constructs a normal-style confidence interval by effectively removing a small, predetermined number of zeros from the data. We propose growth estimators based upon multiplicative adjustments of the sample mean and direct removal of zeros from the sample. These methods do not require estimating the nuisance dispersion parameter. We will demonstrate that the growth estimators' confidence intervals provide improved coverage over a wide range of parameter values and asymptotically converge to the sample mean. Interestingly, the proposed methods succeed despite adding both bias and variance to the normal approximation.

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Saha, Krishna K., Debaraj Sen, and Chun Jin. "Profile likelihood-based confidence interval for the dispersion parameter in count data." Journal of Applied Statistics 39, no. 4 (April 2012): 765–83. http://dx.doi.org/10.1080/02664763.2011.616581.

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Marshall, Peter L., Valerie M. LeMay, and Albert Nussbaum. "Sample size adjustment to reduce the probability of exceeding a specified confidence interval width." Forestry Chronicle 68, no. 6 (December 1, 1992): 747–51. http://dx.doi.org/10.5558/tfc68747-6.

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The maximum confidence interval width desired by a sampler will be exceeded about half the time if sample size is determined using a formula that does not account for variability in the estimate of population dispersion. This probability can be decreased by increasing sample size; however, determining how much to increase sample size can be tedious. A series of graphs is presented that can be used to quickly determine the percentage adjustment for unadjusted sample sizes less than 250 and a significance level of 0.05, assuming simple random sampling with replacement. The benefit of acquiring precise estimates of population dispersion, when it is important not to exceed a specified sampling error level, is clearly demonstrated by comparing the graphs.

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Khooriphan, Wansiri, Sa-Aat Niwitpong, and Suparat Niwitpong. "Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros." PeerJ 10 (September 16, 2022): e14023. http://dx.doi.org/10.7717/peerj.14023.

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The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess zeros treated as a binary random variable is required. Rainfall dispersion is important and interesting, the confidence intervals for the variance of a gamma distribution with excess zeros help to examine rainfall intensity, which may be high or low risk. Herein, we propose confidence intervals for the variance of a gamma distribution with excess zeros by using fiducial quantities and parametric bootstrapping, as well as Bayesian credible intervals and highest posterior density intervals based on the Jeffreys’, uniform, or normal-gamma-beta prior. The performances of the proposed confidence interval were evaluated by establishing their coverage probabilities and average lengths via Monte Carlo simulations. The fiducial quantity confidence interval performed the best for a small probability of the sample containing zero observations (δ) whereas the Bayesian credible interval based on the normal-gamma-beta prior performed the best for large δ. Rainfall data from the Kiew Lom Dam in Lampang province, Thailand, are used to illustrate the efficacies of the proposed methods in practice.

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Yosboonruang, Noppadon, Sa-Aat Niwitpong, and Suparat Niwitpong. "Bayesian computation for the common coefficient of variation of delta-lognormal distributions with application to common rainfall dispersion in Thailand." PeerJ 10 (February 4, 2022): e12858. http://dx.doi.org/10.7717/peerj.12858.

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Rainfall fluctuation makes precipitation and flood prediction difficult. The coefficient of variation can be used to measure rainfall dispersion to produce information for predicting future rainfall, thereby mitigating future disasters. Rainfall data usually consist of positive and true zero values that correspond to a delta-lognormal distribution. Therefore, the coefficient of variation of delta-lognormal distribution is appropriate to measure the rainfall dispersion more than lognormal distribution. In particular, the measurement of the dispersion of precipitation from several areas can be determined by measuring the common coefficient of variation in the rainfall from those areas together. Herein, we compose confidence intervals for the common coefficient of variation of delta-lognormal distributions by employing the fiducial generalized confidence interval, equal-tailed Bayesian credible intervals incorporating the independent Jeffreys or uniform priors, and the method of variance estimates recovery. A combination of the coverage probabilities and expected lengths of the proposed methods obtained via a Monte Carlo simulation study were used to compare their performances. The results show that the equal-tailed Bayesian based on the independent Jeffreys prior was suitable. In addition, it can be used the equal-tailed Bayesian based on the uniform prior as an alternative. The efficacies of the proposed confidence intervals are demonstrated via applying them to analyze daily rainfall datasets from Nan, Thailand.

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Ilut, Cosmin L., and Martin Schneider. "Ambiguous Business Cycles." American Economic Review 104, no. 8 (August 1, 2014): 2368–99. http://dx.doi.org/10.1257/aer.104.8.2368.

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This paper studies a New Keynesian business cycle model with agents who are averse to ambiguity (Knightian uncertainty). Shocks to confidence about future TFP are modeled as changes in ambiguity. To assess the size of those shocks, our estimation uses not only data on standard macro variables, but also incorporates the dispersion of survey forecasts about growth as a measure of confidence. Our main result is that TFP and confidence shocks together can explain roughly two thirds of business cycle frequency movements in the major macro aggregates. Confidence shocks account for about 70 percent of this variation. (JEL D81, D84, E12, E32)

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Rakai, Anikó, and Gergely Kristóf. "Microscale Obstacle Resolving Air Quality Model Evaluation with the Michelstadt Case." Scientific World Journal 2013 (2013): 1–11. http://dx.doi.org/10.1155/2013/781748.

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Modelling pollutant dispersion in cities is challenging for air quality models as the urban obstacles have an important effect on the flow field and thus the dispersion. Computational Fluid Dynamics (CFD) models with an additional scalar dispersion transport equation are a possible way to resolve the flowfield in the urban canopy and model dispersion taking into consideration the effect of the buildings explicitly. These models need detailed evaluation with the method of verification and validation to gain confidence in their reliability and use them as a regulatory purpose tool in complex urban geometries. This paper shows the performance of an open source general purpose CFD code, OpenFOAM for a complex urban geometry, Michelstadt, which has both flow field and dispersion measurement data. Continuous release dispersion results are discussed to show the strengths and weaknesses of the modelling approach, focusing on the value of the turbulent Schmidt number, which was found to give best statistical metric results with a value of 0.7.

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Maneerat, Patcharee, Sa-aat Niwitpong, and Suparat Niwitpong. "A Bayesian approach to construct confidence intervals for comparing the rainfall dispersion in Thailand." PeerJ 8 (February 11, 2020): e8502. http://dx.doi.org/10.7717/peerj.8502.

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Natural disasters such as drought and flooding are the consequence of severe rainfall fluctuation, and rainfall amount data often contain both zero and positive observations, thus making them fit a delta-lognormal distribution. By way of comparison, rainfall dispersion may not be similar in enclosed regions if the topography and the drainage basin are different, so it can be evaluated by the ratio of variances. To estimate this, credible intervals using the highest posterior density based on the normal-gamma prior (HPD-NG) and the method of variance estimates recovery (MOVER) for the ratio of delta-lognormal variances are proposed. Monte Carlo simulation was used to assess the performance of the proposed methods in terms of coverage probability and relative average length. The results of the study reveal that HPD-NG performed very well and was able to meet the requirements in various situations, even with a large difference between the proportions of zeros. However, MOVER is the recommended method for equal small sample sizes. Natural rainfall datasets for the northern and northeastern regions of Thailand are used to illustrate the practical use of the proposed credible intervals.

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Zhu, Zhengqiu, Sihang Qiu, Bin Chen, Rongxiao Wang, and Xiaogang Qiu. "Data-Driven Hazardous Gas Dispersion Modeling Using the Integration of Particle Filtering and Error Propagation Detection." International Journal of Environmental Research and Public Health 15, no. 8 (August 2, 2018): 1640. http://dx.doi.org/10.3390/ijerph15081640.

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The accurate prediction of hazardous gas dispersion process is essential to air quality monitoring and the emergency management of contaminant gas leakage incidents in a chemical cluster. Conventional Gaussian-based dispersion models can seldom give accurate predictions due to inaccurate input parameters and the computational errors. In order to improve the prediction accuracy of a dispersion model, a data-driven air dispersion modeling method based on data assimilation is proposed by applying particle filter to Gaussian-based dispersion model. The core of the method is continually updating dispersion coefficients by assimilating observed data into the model during the calculation process. Another contribution of this paper is that error propagation detection rules are proposed to evaluate their effects since the measured and computational errors are inevitable. So environmental protection authorities can be informed to what extent the model output is of high confidence. To test the feasibility of our method, a numerical experiment utilizing the SF6 concentration data sampled from an Indianapolis field study is conducted. Results of accuracy analysis and error inspection imply that Gaussian dispersion models based on particle filtering and error propagation detection have better performance than traditional dispersion models in practice though sacrificing some computational efficiency.

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Wu, Cheng-I., Yenn-Jiang Lin, I.-Hsin Lee, Men-Tzung Lo, Yu-Cheng Hsieh, Amelia Yun-Yu Chen, Wei-Kai Wang, et al. "Using QRS loop descriptors to characterize the risk of sudden cardiac death in patients with structurally normal hearts." PLOS ONE 17, no. 2 (February 16, 2022): e0263894. http://dx.doi.org/10.1371/journal.pone.0263894.

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The predictive value of non-invasive electrocardiographic examination findings for the risk of sudden cardiac death (SCD) in populations with structurally normal hearts remains unclear. This study aimed to investigate the characteristics of the QRS vectorcardiography of surface electrocardiography in patients with structurally normal hearts who experienced SCD. We consecutively enrolled patients who underwent vectorcardiography between March 2017 and December 2018 in a tertiary referral medical center. These patients didn’t have structural heart diseases, histories of congestive heart failure, or reduced ejection fraction, and they were classified into SCD (with aborted SCD history and cerebral performance category score of 1) and control groups (with an intervention for atrioventricular node reentrant tachycardia and without SCD history). A total of 162 patients (mean age, 54.3±18.1 years; men, 75.9%), including 59 in the SCD group and 103 in the control group, underwent propensity analysis. The baseline demographic variables, underlying diseases, QRS loop descriptors (the percentage of the loop area, loop dispersion, and inter-lead QRS dispersion), and other electrocardiographic parameters were compared between the two groups. In the univariate and multivariate analyses, a smaller percentage of the loop area (odds ratio, 0.0003; 95% confidence interval, 0.00–0.02; p<0.001), more significant V4-5 dispersion (odds ratio, 1.04; 95% confidence interval, 1.02–1.07; p = 0.002), and longer QRS duration (odds ratio, 1.05; 95% confidence interval, 1.00–1.10; p = 0.04) were associated with SCD. In conclusion, the QRS loop descriptors of surface electrocardiography could be used as non-invasive markers to identify patients experiencing aborted SCD from a healthy population. A decreased percentage of loop area and elevated V4-5 QRS dispersion values assessed using vectorcardiography were associated with an increased risk of SCD in patients with structurally normal hearts.

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La-ongkaew, Manussaya, Sa-Aat Niwitpong, and Suparat Niwitpong. "Confidence intervals for the difference between the coefficients of variation of Weibull distributions for analyzing wind speed dispersion." PeerJ 9 (July 2, 2021): e11676. http://dx.doi.org/10.7717/peerj.11676.

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Wind energy is an important renewable energy source for generating electricity that has the potential to replace fossil fuels. Herein, we propose confidence intervals for the difference between the coefficients of variation of Weibull distributions constructed using the concepts of the generalized confidence interval (GCI), Bayesian methods, the method of variance estimates recovery (MOVER) based on Hendricks and Robey’s confidence interval, a percentile bootstrap method, and a bootstrap method with standard errors. To analyze their performances, their coverage probabilities and expected lengths were evaluated via Monte Carlo simulation. The simulation results indicate that the coverage probabilities of GCI were greater than or sometimes close to the nominal confidence level. However, when the Weibull shape parameter was small, the Bayesian- highest posterior density interval was preferable. All of the proposed confidence intervals were applied to wind speed data measured at 90-meter wind energy potential stations at various regions in Thailand.

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Liska, Gilberto Rodrigues, Marcelo Ângelo Citillo, Fortunato Silva de Menezes, and Júlio Silvio de Sousa Bueno Filho. "A simplex dispersion model for improving precision in the odds ratio confidence interval in mixture experiments." Acta Scientiarum. Technology 42 (May 28, 2020): e44068. http://dx.doi.org/10.4025/actascitechnol.v42i1.44068.

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A new approach to data analysis in mixture experiments is proposed using the simplex regression, that is in the class of dispersion models family. The advantages of this approach are illustrated in an experiment studying the mixture effect of fat, carbohydrate, and fiber on tumors’ proportion in mammary glands of rats. Model was evaluated by goodness of fit criteria, simulated envelope charts for residuals of adjusted models, odds ratios graphics and their respective confidence intervals. The simplex regression model showed better quality of fit and smaller odds ratio confidence intervals.

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Chankham, Wasana, Sa-Aat Niwitpong, and Suparat Niwitpong. "Measurement of dispersion of PM 2.5 in Thailand using confidence intervals for the coefficient of variation of an inverse Gaussian distribution." PeerJ 10 (February 17, 2022): e12988. http://dx.doi.org/10.7717/peerj.12988.

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Air pollution is a growing concern for the general public in Thailand with PM 2.5 (particulate matter ≤ 2.5 µm) having the greatest impact on health. The inverse Gaussian (IG) distribution is used for examining the frequency of high concentration events and has often been applied to analyze pollution data, with the coefficient of variation (CV) being used to calculate the quantitative difference in PM 2.5 concentrations. Herein, we propose confidence intervals for the CV of an IG distribution based on the generalized confidence interval (GCI), the adjusted generalized confidence interval (AGCI), the bootstrap percentile confidence interval (BPCI), the fiducial confidence interval (FCI), and the fiducial highest posterior density confidence interval (F-HPDCI). The performance of the proposed confidence intervals was evaluated by using their coverage probabilities and average lengths from various scenarios via Monte Carlo simulations. The simulation results indicate that the coverage probabilities of the AGCI and FCI methods were higher than or close to the nominal level in all of test case scenarios. Moreover, FCI outperformed the others for small sample sizes by achieving the shortest average length. The efficacies of the confidence intervals were demonstrated by using PM 2.5 data from the Din Daeng and Bang Khun Thian districts in Bangkok, Thailand.

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Maneerat, Patcharee, Suparat Niwitpong, and Sa-Aat Niwitpong. "Bayesian confidence intervals for variance of delta-lognormal distribution with an application to rainfall dispersion." Statistics and Its Interface 14, no. 3 (2021): 229–41. http://dx.doi.org/10.4310/20-sii630.

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Cerviño, Miguel. "Resolved and unresolved populations: statistics and synthesis models." Symposium - International Astronomical Union 212 (2003): 545–46. http://dx.doi.org/10.1017/s0074180900212783.

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In this contribution, I present 90%-confidence limits on diagnostic diagrams of Wλ(WR-bump) and L(WR-bump)/L(Hβ) ratio vs.Wλ(Hβ) resulting from evolutionary synthesis models that include the statistical dispersion due to finite stellar populations in real star forming regions.

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Abu-Shawiesh, Moustafa Omar Ahmed, Juthaphorn Sinsomboonthong, and Bhuiyan Mohammad Golam Kibria. "A modified robust confidence interval for the population mean of distribution based on deciles." Statistics in Transition New Series 23, no. 1 (March 1, 2022): 109–28. http://dx.doi.org/10.2478/stattrans-2022-0007.

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Abstract The confidence interval is an important statistical estimator of population location and dispersion parameters. The paper considers a robust modified confidence interval, which is an adjustment of the Student’s t confidence interval based on the decile mean and decile standard deviation for estimating the population mean of a skewed distribution. The efficiency of the proposed interval estimator is evaluated on the basis of an extensive Monte Carlo simulation study. The coverage ratio and average width of the proposed confidence interval are compared with certain existing and widely used confidence intervals. The simulation results show that, in general, the proposed interval estimator’s performance is highly effective. For illustrative purposes, three real-life data sets are analyzed, which, to a certain extent, support the findings obtained from the simulation study. Thus, we recommend that practitioners use the robust modified confidence interval for estimating the population mean when the data are generated by a normal or skewed distribution.

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Cheng, Ji, Ping Jiang, Qi Zhou, Jiexiang Hu, Tao Yu, Leshi Shu, and Xinyu Shao. "A lower confidence bounding approach based on the coefficient of variation for expensive global design optimization." Engineering Computations 36, no. 3 (April 8, 2019): 830–49. http://dx.doi.org/10.1108/ec-08-2018-0390.

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PurposeEngineering design optimization involving computational simulations is usually a time-consuming, even computationally prohibitive process. To relieve the computational burden, the adaptive metamodel-based design optimization (AMBDO) approaches have been widely used. This paper aims to develop an AMBDO approach, a lower confidence bounding approach based on the coefficient of variation (CV-LCB) approach, to balance the exploration and exploitation objectively for obtaining a global optimum under limited computational budget.Design/methodology/approachIn the proposed CV-LCB approach, the coefficient of variation (CV) of predicted values is introduced to indicate the degree of dispersion of objective function values, while the CV of predicting errors is introduced to represent the accuracy of the established metamodel. Then, a weighted formula, which takes the degree of dispersion and the prediction accuracy into consideration, is defined based on the already-acquired CV information to adaptively update the metamodel during the optimization process.FindingsTen numerical examples with different degrees of complexity and an AIAA aerodynamic design optimization problem are used to demonstrate the effectiveness of the proposed CV-LCB approach. The comparisons between the proposed approach and four existing approaches regarding the computational efficiency and robustness are made. Results illustrate the merits of the proposed CV-LCB approach in computational efficiency and robustness.Practical implicationsThe proposed approach exhibits high efficiency and robustness in engineering design optimization involving computational simulations.Originality/valueCV-LCB approach can balance the exploration and exploitation objectively.

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Yosboonruang, Noppadon, Sa-aat Niwitpong, and Suparat Niwitpong. "Measuring the dispersion of rainfall using Bayesian confidence intervals for coefficient of variation of delta-lognormal distribution: a study from Thailand." PeerJ 7 (July 22, 2019): e7344. http://dx.doi.org/10.7717/peerj.7344.

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Since rainfall data series often contain zero values and thus follow a delta-lognormal distribution, the coefficient of variation is often used to illustrate the dispersion of rainfall in a number of areas and so is an important tool in statistical inference for a rainfall data series. Therefore, the aim in this paper is to establish new confidence intervals for a single coefficient of variation for delta-lognormal distributions using Bayesian methods based on the independent Jeffreys’, the Jeffreys’ Rule, and the uniform priors compared with the fiducial generalized confidence interval. The Bayesian methods are constructed with either equitailed confidence intervals or the highest posterior density interval. The performance of the proposed confidence intervals was evaluated using coverage probabilities and expected lengths via Monte Carlo simulations. The results indicate that the Bayesian equitailed confidence interval based on the independent Jeffreys’ prior outperformed the other methods. Rainfall data recorded in national parks in July 2015 and in precipitation stations in August 2018 in Nan province, Thailand are used to illustrate the efficacy of the proposed methods using a real-life dataset.

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Nicolae, Victor, Alexandru Dandocsi, Luminita Marmureanu, and Camelia Talianu. "Biomass burning aerosol over Romania using dispersion model and Calipso data." EPJ Web of Conferences 176 (2018): 04012. http://dx.doi.org/10.1051/epjconf/201817604012.

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The purpose of the study is to analyze the seasonal variability, for the hot and cold seasons, of biomass burning aerosol observed over Romania using forward dispersion calculations based on FLEXPART model. The model was set up to use as input the MODIS fire data with a degree of confidence over 25% after transforming the emitted power in emission rate. The modelled aerosols in this setup was black carbon coated by organics. Distribution in the upper layers were compared to Calipso retrieval.

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Bridges, Terry, Keith Ashman, Mike Beasley, Doug Geisler, Dave Hanes, Ray Sharpies, and Steve Zepf. "Globular Clusters as Probes of the Virgo gE NGC 4472." Symposium - International Astronomical Union 201 (2005): 441–42. http://dx.doi.org/10.1017/s0074180900216574.

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We present radial velocities for 144 globular clusters (GCs) around the Virgo gE NGC 4472 (M49), and ages and metallicities for 131 GCs. We confirm our earlier finding that the metal-poor GCs have a significantly higher velocity dispersion than the metal-rich GCs, and we find little or no rotation in the metal-rich GCs. The velocity dispersion profile is consistent with isotropic GC orbits and the mass distribution inferred from X-ray data. Our sample of GCs spans a metallicity range of −1.6 ≤ [Fe/H] ≤ 0 dex. The metal-poor and metal-rich GCs are coeval within the errors, and all GCs older than 6 Gyr at 95% confidence.

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Cox, Raymond, Ajit Dayanandan, Han Donker, and John R. Nofsinger. "Confucius confusion: analyst forecast dispersion and business cycles." Review of Behavioral Finance 10, no. 2 (June 11, 2018): 130–45. http://dx.doi.org/10.1108/rbf-04-2017-0041.

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PurposeFinancial analysts have been found to be overconfident. The purpose of this paper is to study the ramifications of that overconfidence on the dispersion of earnings estimates as a predictor of the US business cycle.Design/methodology/approachWhether aggregate analyst forecast dispersion contains information about turning points in business cycles, especially downturns, is examined by utilizing the analyst earnings forecast dispersion metric. The primary analysis derives from logit regression and Markov switching models. The analysis controls for sentiment (consumer confidence), output (industrial production), and financial indicators (stock returns and turnover). Analyst data come from Institutional Brokers Estimate System, while the economic data are available at the Federal Reserve Bank of St Louis Economic Data site.FindingsA rise in the dispersion of analyst forecasts is a significant predictor of turning points in the US business cycle. Financial analyst uncertainty of earnings estimate contains crucial information about the risks of US business cycle turning points. The results are consistent with some analysts becoming overconfident during the expansion period and misjudging the precision of their information, thus over or under weighting various sources of information. This causes the disagreement among analysts measured as dispersion.Originality/valueThis is the first study to show that analyst forecast dispersion contributions valuable information to predictions of economic downturns. In addition, that dispersion can be attributed to analyst overconfidence.

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Izumiura, H., T. Ono, I. Yamamura, K. Okumura, T. Onaka, S. Deguchi, N. Ukita, O. Hashimoto, and Y. Nakada. "SIO maser survey of the Bulge IRAS sources." Symposium - International Astronomical Union 153 (1993): 303–8. http://dx.doi.org/10.1017/s0074180900123368.

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SiO maser emission from the Bulge IRAS sources has been searched by the v=1, J=1−0 and v=2, J=1—0 transitions to investigate the kinematics of the Galactic Bulge, resulting in a sample of 124 line-of-sight velocities. The rotation velocity, velocity dispersion, and velocity offset at l = 0° for the sample are found to be , and —18.2±9.7 km s−1, respectively (80% confidence interval). Furthermore we find trends for the rotation velocity and velocity dispersion to decrease with distance from the galactic plane. These trends are supported by a larger sample constructed by incorporating other available velocity data on the Bulge IRAS sources. The rotation velocity and velocity dispersion are expressed as 15.6—1.23x|b(deg)| km s−1 deg−1 and 101−3.6x |b(deg)| km s−1, respectively. The implications of the observed quantities are discussed.

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Emsellem, Eric, Remco F. J. van der Burg, Jérémy Fensch, Tereza Jeřábková, Anita Zanella, Adriano Agnello, Michael Hilker, et al. "The ultra-diffuse galaxy NGC 1052-DF2 with MUSE." Astronomy & Astrophysics 625 (May 2019): A76. http://dx.doi.org/10.1051/0004-6361/201834909.

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The so-called ultra-diffuse galaxy NGC 1052-DF2 was announced to be a galaxy lacking dark matter based on a spectroscopic study of its constituent globular clusters. Here we present the first spectroscopic analysis of the stellar body of this galaxy using the MUSE integral-field spectrograph at the (ESO) Very Large Telescope. The MUSE datacube simultaneously provides DF2’s stellar velocity field and systemic velocities for seven globular clusters (GCs). We further discovered three planetary nebulae (PNe) that are likely part of this galaxy. While five of the clusters had velocities measured in the literature, we were able to confirm the membership of two more candidates through precise radial velocity measurements, which increases the measured specific frequency of GCs in DF2. The mean velocity of the diffuse stellar body, 1792.9+1.4−1.8 km s−1, is consistent with the mean globular cluster velocity. We detect a weak but significant velocity gradient within the stellar body, with a kinematic axis close to the photometric major axis, making it a prolate-like rotator. We estimate a velocity dispersion from the clusters and PNe of σint = 10.6−2.3+3.9 km s−1. The velocity dispersion σDF2⋆(Re) for the stellar body within one effective radius is 10.8+3.2−4.0 km s−1. Considering various sources of systemic uncertainties, this central value varies between 5 and 13 km s−1, and we conservatively report a 95% confidence upper limit to the dispersion within one Re of 21 km s−1. We provide updated mass estimates based on these dispersions corresponding to the different distances to NGC 1052-DF2 that have been reported in the recent literature.

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Khooriphan, Wansiri, Sa-Aat Niwitpong, and Suparat Niwitpong. "Confidence Intervals for the Ratio of Variances of Delta-Gamma Distributions with Applications." Axioms 11, no. 12 (November 30, 2022): 689. http://dx.doi.org/10.3390/axioms11120689.

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Since rainfall data often contain zero observations, the ratio of the variances of delta-gamma distributions can be used to compare the rainfall dispersion between two rainfall datasets. To this end, we constructed the confidence interval for the ratio of the variances of two delta-gamma distributions by using the fiducial quantity method, Bayesian credible intervals based on the Jeffreys, uniform, or normal-gamma-beta priors, and highest posterior density (HPD) intervals based on the Jeffreys, uniform, or normal-gamma-beta priors. The performances of the proposed confidence interval methods were evaluated in terms of their coverage probabilities and average lengths via Monte Carlo simulation. Our findings show that the HPD intervals based on Jeffreys prior and the normal-gamma-beta prior are both suitable for datasets with a small and large probability of containing zeros, respectively. Rainfall data from Phrae province, Thailand, are used to illustrate the practicability of the proposed methods with real data.

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Puggard, Wisunee, Sa-Aat Niwitpong, and Suparat Niwitpong. "Comparison Analysis on the Coefficients of Variation of Two Independent Birnbaum-Saunders Distributions by Constructing Confidence Intervals for the Ratio of Coefficients of Variation." Sains Malaysiana 51, no. 7 (July 31, 2022): 2265–81. http://dx.doi.org/10.17576/jsm-2022-5107-26.

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The fatigue failure of materials can be investigated by applying the Birnbaum-Saunders (BS) distribution to fatigue failure datasets. The coefficient of variation (CV) is an important descriptive statistic that is widely used to measure the dispersion of data. In addition, for two independent datasets following BS distributions, the ratio of their CVs can be used to compare their CVs, especially when the difference is small, and constructing confidence intervals for this scenario is of interest in this study. Hence, we propose new confidence intervals for the ratio of the CVs from two BS distributions by using the bootstrap confidence interval (BCI), the fiducial generalized confidence interval (FGCI), a Bayesian credible interval (BayCI), and the highest posterior density (HPD) interval approaches. The performances of the proposed confidence intervals were compared with the generalized confidence interval (GCI) in terms of their coverage probabilities and average lengths via Monte Carlo simulations. The results indicate that the HPD interval outperformed the others when the coverage probabilities and the average lengths were both considered together. The efficacies of the proposed methods and GCI are illustrated using real datasets of the fatigue life of 6061-T6 aluminum coupons.

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Thangjai, Warisa, and Suparat Niwitpong. "Comparing particulate matter dispersion in Thailand using the Bayesian Confidence Intervals for ratio of coefficients of variation." Statistics in Transition New Series 21, no. 5 (2020): 41–60. http://dx.doi.org/10.21307/stattrans-2020-054.

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Harvey, Natalie J., Helen F. Dacre, Cameron Saint, Andrew T. Prata, Helen N. Webster, and Roy G. Grainger. "Quantifying the impact of meteorological uncertainty on emission estimates and the risk to aviation using source inversion for the Raikoke 2019 eruption." Atmospheric Chemistry and Physics 22, no. 13 (July 5, 2022): 8529–45. http://dx.doi.org/10.5194/acp-22-8529-2022.

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Abstract. Due to the remote location of many volcanoes, there is substantial uncertainty about the timing, amount and vertical distribution of volcanic ash released when they erupt. One approach to determine these properties is to combine prior estimates with satellite retrievals and simulations from atmospheric dispersion models to create posterior emission estimates, constrained by both the observations and the prior estimates, using a technique known as source inversion. However, the results are dependent not only on the accuracy of the prior assumptions, the atmospheric dispersion model and the observations used, but also on the accuracy of the meteorological data used in the dispersion simulations. In this study, we advance the source inversion approach by using an ensemble of meteorological data from the Met Office Global and Regional Ensemble Prediction System to represent the uncertainty in the meteorological data and apply it to the 2019 eruption of Raikoke. Retrievals from the Himawari-8 satellite are combined with NAME dispersion model simulations to create posterior emission estimates. The use of ensemble meteorology provides confidence in the posterior emission estimates and associated dispersion simulations that are used to produce ash forecasts. Prior mean estimates of fine volcanic ash emissions for the Raikoke eruption based on plume height observations are more than 15 times higher than any of the mean posterior ensemble estimates. In addition, the posterior estimates have a different vertical distribution, with 27 %–44 % of ash being emitted into the stratosphere compared to 8 % in the mean prior estimate. This has consequences for the long-range transport of ash, as deposition to the surface from this region of the atmosphere happens over long timescales. The posterior ensemble spread represents uncertainty in the inversion estimate of the ash emissions. For the first 48 h following the eruption, the prior ash column loadings lie outside an estimate of the error associated with a set of independent satellite retrievals, whereas the posterior ensemble column loadings do not. Applying a risk-based methodology to an ensemble of dispersion simulations using the posterior emissions shows that the area deemed to be of the highest risk to aviation, based on the fraction of ensemble members exceeding predefined ash concentration thresholds, is reduced by 49 %. This is compared to estimates using an ensemble of dispersion simulations using the prior emissions with ensemble meteorology. If source inversion had been used following the eruption of Raikoke, it would have had the potential to significantly reduce disruptions to aviation operations. The posterior inversion emission estimates are also sensitive to uncertainty in other eruption source parameters and internal dispersion model parameters. Extending the ensemble inversion methodology to account for uncertainty in these parameters would give a more complete picture of the emission uncertainty, further increasing confidence in these estimates.

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Nikolic, Ljubisa, Vesna Nikolic, Vlada Veljkovic, Miodrag Lazic, and Dejan Skala. "Axial dispersion of the liquid phase on a three-phase Karr reciprocating plate column." Journal of the Serbian Chemical Society 69, no. 7 (2004): 581–99. http://dx.doi.org/10.2298/jsc0407581n.

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The influence of the gas flow rate and vibration intensity in the presence of the solid phase (polypropylene spheres) on axial mixing of the liquid phase in a three phase (gas-liquid-solid) Karr reciprocating plate column (RPC) was investigated. Assuming that the dispersionmodel of liquid flow could be used for the real situation inside the column, the dispersion coefficient of the liquid phase was determined as a function of different operating parameters. For a two-phase liquid-solid RPC the following correlation was derived: DL = 1.26(Af)1.42 UL 0.51 ?S 0.23 and a similar equation could be applied with ? 30 % confidence for the calculation of axial dispersion in the case of a three-phase RPC: DL = 1.39(Af)0.47 UL0.42UG0.03 ?S -0.26.

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Short, Meghan I., Howard J. Cabral, Janice M. Weinberg, Michael P. LaValley, and Joseph M. Massaro. "A novel confidence interval for a single proportion in the presence of clustered binary outcome data." Statistical Methods in Medical Research 29, no. 1 (January 23, 2019): 111–21. http://dx.doi.org/10.1177/0962280218823231.

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Estimating the precision of a single proportion via a 100(1−α)% confidence interval in the presence of clustered data is an important statistical problem. It is necessary to account for possible over-dispersion, for instance, in animal-based teratology studies with within-litter correlation, epidemiological studies that involve clustered sampling, and clinical trial designs with multiple measurements per subject. Several asymptotic confidence interval methods have been developed, which have been found to have inadequate coverage of the true proportion for small-to-moderate sample sizes. In addition, many of the best-performing of these intervals have not been directly compared with regard to the operational characteristics of coverage probability and empirical length. This study uses Monte Carlo simulations to calculate coverage probabilities and empirical lengths of five existing confidence intervals for clustered data across various true correlations, true probabilities of interest, and sample sizes. In addition, we introduce a new score-based confidence interval method, which we find to have better coverage than existing intervals for small sample sizes under a wide range of scenarios.

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Haywood-Alexander, Marcus, Nikolaos Dervilis, Keith Worden, Robin S. Mills, Purim Ladpli, and Timothy J. Rogers. "A Bayesian Method for Material Identification of Composite Plates via Dispersion Curves." Sensors 23, no. 1 (December 24, 2022): 185. http://dx.doi.org/10.3390/s23010185.

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Ultrasonic guided waves offer a convenient and practical approach to structural health monitoring and non-destructive evaluation. A key property of guided waves is the fully defined relationship between central frequency and propagation characteristics (phase velocity, group velocity and wavenumber)—which is described using dispersion curves. For many guided wave-based strategies, accurate dispersion curve information is invaluable, such as group velocity for localisation. From experimental observations of dispersion curves, a system identification procedure can be used to determine the governing material properties. As well as returning an estimated value, it is useful to determine the distribution of these properties based on measured data. A method of simulating samples from these distributions is to use the iterative Markov-Chain Monte Carlo (MCMC) procedure, which allows for freedom in the shape of the posterior. In this work, a scanning-laser Doppler vibrometer is used to record the propagation of Lamb waves in a unidirectional-glass-fibre composite plate, and dispersion curve data for various propagation angles are extracted. Using these measured dispersion curve data, the MCMC sampling procedure is performed to provide a Bayesian approach to determining the dispersion curve information for an arbitrary plate. The distribution of the material properties at each angle is discussed, including the inferred confidence in the predicted parameters. The percentage errors of the estimated values for the parameters were 10-15 points larger when using the most likely estimates, as opposed to calculating from the posterior distributions, highlighting the advantages of using a probabilistic approach.

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Nuñez de Arenas-Arroyo, Sergio, Vicente Martínez-Vizcaíno, Iván Cavero-Redondo, Celia Álvarez-Bueno, Sara Reina-Gutierrez, and Ana Torres-Costoso. "The Effect of Neurodynamic Techniques on the Dispersion of Intraneural Edema: A Systematic Review with Meta-Analysis." International Journal of Environmental Research and Public Health 19, no. 21 (November 4, 2022): 14472. http://dx.doi.org/10.3390/ijerph192114472.

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Background: There is evidence for the positive effects of neurodynamic techniques in some peripheral entrapment neuropathies, but the rationale for these effects has not been validated. We aimed to estimate the direct effect of neurodynamic techniques on the dispersion of artificially induced intraneural edema measured by dye spread in cadavers. Methods: We systematically searched the MEDLINE, WOS, Scopus, and the Cochrane databases from inception to February 2020 for experimental studies addressing the efficacy of neurodynamic techniques on the dispersion of artificially induced intraneural edema. The DerSimonian and Laird method was used to compute pooled estimates of the mean differences (MDs) and its respective 95% confidence intervals (CIs). Subgroup analyses were conducted according to the type of neurodynamic technique. In addition, a 95% prediction interval was calculated to reflect the variation in true treatment effects in different settings, including the effect to be expected in future patients. Results: Pooled results showed a significant increase in fluid dispersion (MD = 2.57 mm; 95%CI: 1.13 to 4.01). Subgroup analysis showed increased dye spread in the tensioning techniques group (MD = 2.22 mm; 95%CI: 0.86 to 3.57). Conclusion: Neurodynamic techniques improved the intraneural edema dispersion and should be considered for the management of peripheral compression neuropathies. Furthermore, tensioning techniques appear to be effective in helping to disperse intraneural edema.

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Kowalski, Andrzej, and Eligiusz Jędrzejec. "Influence Of Subsidence Fluctuation On The Determination Of Mining Area Curvatures." Archives of Mining Sciences 60, no. 2 (June 1, 2015): 487–505. http://dx.doi.org/10.1515/amsc-2015-0032.

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Abstract The article concerns the random dispersion of deformation indicators, especially the influence of subsidence fluctuation on the distribution of inclinations and curvatures. Surface curvatures have significant influence on building objects. The article includes the probability studies of displacement fluctuation for two arbitrarily close but different points. It was determined, if the probability is dependent on each other or not. Therefore, the separate deformation indicators can be considered to damage hazard assessment of building objects, if their standard variation of fluctuation is well determined (dependent on the fluctuation of vertical and horizontal displacements). Consequently, it is possible to determine the confidence intervals of fluctuation for all separate deformation indicators. Even in a case of low values of predicted separate curvatures, their values can be significant higher when considering their natural dispersion.

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Yosboonruang, Noppadon, and Sa-Aat Niwitpong. "Confidence Intervals for the Coefficient of Quartile Variation of a Zero-inflated Lognormal Distribution." Emerging Science Journal 5, no. 4 (August 1, 2021): 457–70. http://dx.doi.org/10.28991/esj-2021-01289.

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There are many types of skewed distribution, one of which is the lognormal distribution that is positively skewed and may contain true zero values. The coefficient of quartile variation is a statistical tool used to measure the dispersion of skewed and kurtosis data. The purpose of this study is to establish confidence and credible intervals for the coefficient of quartile variation of a zero-inflated lognormal distribution. The proposed approaches are based on the concepts of the fiducial generalized confidence interval, and the Bayesian method. Coverage probabilities and expected lengths were used to evaluate the performance of the proposed approaches via Monte Carlo simulation. The results of the simulation studies show that the fiducial generalized confidence interval and the Bayesian based on uniform and normal inverse Chi-squared priors were appropriate in terms of the coverage probability and expected length, while the Bayesian approach based on Jeffreys' rule prior can be used as alternatives. In addition, real data based on the red cod density from a trawl survey in New Zealand is used to illustrate the performances of the proposed approaches. Doi: 10.28991/esj-2021-01289 Full Text: PDF

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Puggard, Wisunee, Sa-Aat Niwitpong, and Suparat Niwitpong. "Confidence Intervals for Comparing the Variances of Two Independent Birnbaum–Saunders Distributions." Symmetry 14, no. 7 (July 21, 2022): 1492. http://dx.doi.org/10.3390/sym14071492.

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Fatigue in a material occurs when it is subjected to fluctuating stress and strain, which usually results in failure due to the accumulated damage. In statistics, asymmetric distribution, which is commonly used for describing the fatigue life of materials, is the Birnbaum–Saunders (BS) distribution. This distribution can be transform to the normal distribution, which is symmetrical. Furthermore, variance is used to examine the dispersion of the fatigue life data. However, comparing the variances of two independent samples that follow BS distributions has not previously been reported. To accomplish this, we propose methods for providing the confidence interval for the ratio of variances of two independent BS distributions based on the generalized fiducial confidence interval (GFCI), a Bayesian credible interval (BCI), and the highest posterior density (HPD) intervals based on a prior distribution with partial information (HPD-PI) and a proper prior with known hyperparameters (HPD-KH). A Monte Carlo simulation study was carried out to examine the efficacies of the methods in terms of their coverage probabilities and average lengths. The simulation results indicate that the HPD-PI performed satisfactorily for all sample sizes investigated. To illustrate the efficacies of the proposed methods with real data, they were also applied to study the confidence interval for the ratio of the variances of two 6061-T6 aluminum coupon fatigue-life datasets.

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Leroy, D., J. M. Giovannoni, and L. Y. Maystre. "Sampling Method To Determine a Household Waste Composition Variance." Waste Management & Research: The Journal for a Sustainable Circular Economy 10, no. 1 (January 1992): 3–12. http://dx.doi.org/10.1177/0734242x9201000102.

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Knowledge of waste composition is of crucial importance for waste management forecasting. Composition is usually specified by average content of glass, paper, organic matter etc. In this paper a sorting method and its application to variance determination is described. A variation coefficient and a confidence interval are then calculated. From these two parameters an appreciation of the dispersion and the uncertainty associated with the mean values can be derived. In the case studied, the variation coefficients calculated were between 0.10 and 0.50 depending on the class of waste. Analysis of confidence intervals shows that reliability is good for low-abundance components such as, for example, aluminium, iron and plastics. The influence of practical constraints on the theoretical guidelines is also discussed.

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Longeard, Nicolas, Nicolas Martin, Rodrigo A. Ibata, Else Starkenburg, Pascale Jablonka, David S. Aguado, Raymond G. Carlberg, et al. "The pristine dwarf-galaxy survey – III. Revealing the nature of the Milky Way globular cluster Sagittarius II." Monthly Notices of the Royal Astronomical Society 503, no. 2 (March 5, 2021): 2754–62. http://dx.doi.org/10.1093/mnras/stab604.

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ABSTRACT We present a new spectroscopic study of the faint Milky Way satellite Sagittarius II. Using multiobject spectroscopy from the Fibre Large Array Multi-Element Spectrograph, we supplement the data set of Longeard et al. with 47 newly observed stars, 19 of which are identified as members of the satellite. These additional member stars are used to put tighter constraints on the dynamics and the metallicity properties of the system. We find a low velocity dispersion of $\sigma _\mathrm{v}^\mathrm{SgrII} = 1.7 \pm 0.5$ km s−1, in agreement with the dispersion of Milky Way globular clusters of similar luminosity. We confirm the very metal-poor nature of the satellite ([Fe/H]$_\mathrm{spectro}^\mathrm{SgrII} = -2.23 \pm 0.07$) and find that the metallicity dispersion of Sgr II is not resolved, reaching only 0.20 at the 95 per cent confidence limit. No star with a metallicity below −2.5 is confidently detected. Therefore, despite the unusually large size of the system (r$_h = 35.5 ^{+1.4}_{-1.2}$ pc), we conclude that Sgr II is an old and metal-poor globular cluster of the Milky Way.

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Maneerat, Patcharee, Pisit Nakjai, and Sa-Aat Niwitpong. "Estimation methods for the ratio of medians of three-parameter lognormal distributions containing zero values and their application to wind speed data from northern Thailand." PeerJ 10 (October 11, 2022): e14194. http://dx.doi.org/10.7717/peerj.14194.

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Wind speed has an important impact on the formation and dispersion of fine particulate matter (PM), which can cause several health problems. During the transition from the winter to the summer season in northern Thailand, the wind speed has been low for longer than usual, which has resulted in fine PM accumulating in the air. Motivated by this, we have identified a need to investigate wind speed due to its effect on PM formation and dispersion and to raise awareness among the general public. The hourly windspeed can be approximated by using confidence intervals for the ratio of the medians of three-parameter lognormal distributions containing zero values. Thus, we constructed them by using fiducial, normal approximation, and Bayesian methods. By way of comparison, the performance measures for all ofthe proposed methods (the coverage percentage, lower and upper error probabilities (LEP and UEP,respectively), and expected length) were assessed via Monte Carlo simulation. The results of Monte Carlo simulation studies show that the Bayesian method provided coverage percentages close to the nominal confidence level and shorter intervals than the other methods. Importantly, it maintained a good balance between LEP and UEP even for large variation and percentage of zero-valued observations. To illustrate the efficacy of our proposed methods, we applied them to hourly wind speed data from northern Thailand.

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Chow, Fotini Katopodes, Branko Kosović, and Stevens Chan. "Source Inversion for Contaminant Plume Dispersion in Urban Environments Using Building-Resolving Simulations." Journal of Applied Meteorology and Climatology 47, no. 6 (June 1, 2008): 1553–72. http://dx.doi.org/10.1175/2007jamc1733.1.

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Abstract The ability to determine the source of a contaminant plume in urban environments is crucial for emergency-response applications. Locating the source and determining its strength based on downwind concentration measurements, however, are complicated by the presence of buildings that can divert flow in unexpected directions. High-resolution flow simulations are now possible for predicting plume evolution in complex urban geometries, where contaminant dispersion is affected by the flow around individual buildings. Using Bayesian inference via stochastic sampling algorithms with a high-resolution computational fluid dynamics model, an atmospheric release event can be reconstructed to determine the plume source and release rate based on point measurements of concentration. Event-reconstruction algorithms are applied first for flow around a prototype isolated building (a cube) and then using observations and flow conditions from Oklahoma City, Oklahoma, during the Joint Urban 2003 field campaign. Stochastic sampling methods (Markov chain Monte Carlo) are used to extract likely source parameters, taking into consideration measurement and forward model errors. In all cases the steady-state flow field generated by a 3D Navier–Stokes finite-element code (FEM3MP) is used to drive thousands of forward-dispersion simulations. To enhance computational performance in the inversion procedure, a reusable database of dispersion simulation results is created. It is possible to successfully invert the dispersion problems to determine the source location and release rate to within narrow confidence intervals even with such complex geometries. The stochastic methodology here is general and can be used for time-varying release rates and reactive flow conditions. The results of inversion indicate the probability of a source being found at a particular location with a particular release rate, thus inherently reflecting uncertainty in observed data or the lack of enough data in the shape and size of the probability distribution. A composite plume showing concentrations at the desired confidence level can also be constructed using the realizations from the reconstructed probability distribution. This can be used by emergency responders as a tool to determine the likelihood of concentration at a particular location being above a threshold value.

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Thangjai, Warisa, Sa-Aat Niwitpong, and Suparat Niwitpong. "Confidence intervals for the common coefficient of variation of rainfall in Thailand." PeerJ 8 (September 21, 2020): e10004. http://dx.doi.org/10.7717/peerj.10004.

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The log-normal distribution is often used to analyze environmental data like daily rainfall amounts. The rainfall is of interest in Thailand because high variable climates can lead to periodic water stress and scarcity. The mean, standard deviation or coefficient of variation of the rainfall in the area is usually estimated. The climate moisture index is the ratio of plant water demand to precipitation. The climate moisture index should use the coefficient of variation instead of the standard deviation for comparison between areas with widely different means. The larger coefficient of variation indicates greater dispersion, whereas the lower coefficient of variation indicates the lower risk. The common coefficient of variation, is the weighted coefficients of variation based on k areas, presents the average daily rainfall. Therefore, the common coefficient of variation is used to describe overall water problems of k areas. In this paper, we propose four novel approaches for the confidence interval estimation of the common coefficient of variation of log-normal distributions based on the fiducial generalized confidence interval (FGCI), method of variance estimates recovery (MOVER), computational, and Bayesian approaches. A Monte Carlo simulation was used to evaluate the coverage probabilities and average lengths of the confidence intervals. In terms of coverage probability, the results show that the FGCI approach provided the best confidence interval estimates for most cases except for when the sample case was equal to six populations (k = 6) and the sample sizes were small (nI < 50), for which the MOVER confidence interval estimates were the best. The efficacies of the proposed approaches are illustrated with example using real-life daily rainfall datasets from regions of Thailand.

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Smith, T. K., and M. N. Ingham. "The Viability of XRF Determination of Gold in Mineral Reconnaissance." Advances in X-ray Analysis 32 (1988): 227–31. http://dx.doi.org/10.1154/s0376030800020516.

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Commercial interest in gold is persistent and resurgent, and there is a consequent need for reappraisal of its methods of analysis. Because its modes of occurrence often manifest themselves in irregular dispersion and low concentration, special care must be taken in sampling and analysis. A sufficient amount of the initial sample must be taken to ensure adequate representation, and preconcentration is often necessary to elevate the metal content to a confidence level high enough above the detection limit for the analytical technique.

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Ha, Raegyung, Amarjargal Baatar, and Yongjae Yu. "Identification of atmospheric transport and dispersion of Asian dust storms." Natural Hazards and Earth System Sciences 17, no. 8 (August 29, 2017): 1425–35. http://dx.doi.org/10.5194/nhess-17-1425-2017.

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Abstract. Backward trajectories of individual Asian dust storm (ADS) events were calculated using the Hybrid Single Particle Lagrangian Integrated Trajectory (HYSPLIT) at four representative stations in Korea. A total of 743 ADS events and associated 2229 (endings of altitudes at 1000, 1500, and 2000 m per ADS event) backward trajectories from four stations were traced from January 2003 to August 2015. Regardless of the locations of the observed stations and the threshold time divide, a recent increase in the ADS occurrence rate was statistically significant with a 99.9 % confidence limit. Winter and spring were high-occurrence seasons for the ADS, while it rarely occurred in summer. Angular distributions of dust transport indicated a dominance of northwesterly wind, as more than two-thirds of ADS events are azimuthally confined from 290 to 340°. In addition, there is a tendency for stronger PM10 dust air concentration to be from the northwest. We found a strong inverse correlation between the number of days with ADS events and cumulative PM10 dust air concentration, indicating that the total amount of cumulative PM10 discharge was rather constant over time. If so, relatively shorter transport distances and a more continental dust passage over the Shandong peninsular would yield less PM10 in a shorter transport path but with a stronger concentration.

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Anderson, H. Glenn, Michael G. Kendrach, and Shana Trice. "Understanding Statistical and Clinical Significance: Hypothesis Testing." Journal of Pharmacy Practice 11, no. 3 (June 1998): 181–95. http://dx.doi.org/10.1177/089719009801100309.

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This primer reviews a number of statistical concepts integral to the hypothesis testing process and its role in decision making. Concepts of variables, scales of measure, and measures of central tendency and dispersion are discussed, and a 5-step process of hypothesis testing is presented. Finally, a discussion of the statistical and clinical significance of research results is presented, along with the concept of confidence intervals as a method of conveying information about the effect size as well as the statistical significance of a difference between groups.

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Journal articles on the topic 'Confidence dispersion'

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