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Artykuły w czasopismach na temat „Empirical distribution function test”

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Autor: Grafiati

Data publikacji: 4 czerwca 2021

Data aktualizacji: 20 lutego 2023

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1

Liu, Yingxi, i Ahmed Tewfik. "Empirical Likelihood Ratio Test With Distribution Function Constraints". IEEE Transactions on Signal Processing 61, nr 18 (wrzesień 2013): 4463–72. http://dx.doi.org/10.1109/tsp.2013.2271484.

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SKAUG, HANS JULIUS, i DAG TJØSTHEIM. "A nonparametric test of serial independence based on the empirical distribution function". Biometrika 80, nr 3 (1993): 591–602. http://dx.doi.org/10.1093/biomet/80.3.591.

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3

Pospelov, Boris, Vladimir Andronov, Evgenіy Rybka, Yuliia Bezuhla, Olena Liashevska, Tetiana Butenko, Eleonora Darmofal, Svitlana Hryshko, Iryna Kozynska i Yurii Bielashov. "Empirical cumulative distribution function of the characteristic sign of the gas environment during fire". Eastern-European Journal of Enterprise Technologies 4, nr 10 (118) (30.08.2022): 60–66. http://dx.doi.org/10.15587/1729-4061.2022.263194.

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The object of this study is the dynamics of a characteristic sign of an increment in the state of the gaseous medium in the premises when a thermal source of fire appears. The subject of the study is the type of an empirical cumulative function of the distribution of dynamics of a characteristic sign of an increment in the state of the gaseous medium in the absence and appearance of a thermal source of fire in the premises. As a characteristic feature, the probability of non-recurrence of the increments of the vector of states of the gaseous medium was chosen. The results of the study make it possible to quickly identify thermal sources of fire under uncertain conditions. The methodology for studying the empirical cumulative function of the distribution of the dynamics of the probability of non-recurrence of the increments of the vector of the state of the gas medium has been substantiated. The technique includes the implementation of seven consecutive procedures and makes it possible to explore the specified function for arbitrary time intervals. The empirical cumulative distribution function for two fixed time intervals of equal duration before and after the appearance of test thermal sources of fire in the laboratory chamber was investigated. It was established that the features of the empirical cumulative functions of the distribution of the dynamics of the probability of non-recurrence of the increments of the vector of the state of the gas environment allow for early detection of fire. The main sign of detection is a decrease in the fixed values of the empirical cumulative distribution function. For test thermal sources, fixed values of the empirical cumulative distribution function are in the range of 0.15–0.44. These probabilities are determined by the different ignition rate of the test thermal sources. The research results indicate the possibility of using the identified features of empirical cumulative distribution functions of the dynamics of the probability of non-recurrence of increments of the vector of the state of the gas environment for the early detection of fires

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4

Liu, Xiaohui, Qihua Wang i Yi Liu. "A consistent jackknife empirical likelihood test for distribution functions". Annals of the Institute of Statistical Mathematics 69, nr 2 (1.02.2016): 249–69. http://dx.doi.org/10.1007/s10463-015-0550-9.

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5

MEINTANIS, SIMOS, i I. A. KOUTROUVELIS. "TESTING THE FIT TO GENERALIZED POISSON DISTRIBUTIONS BASED ON AN EMPIRICAL TRANSFORM". International Journal of Reliability, Quality and Safety Engineering 08, nr 01 (marzec 2001): 59–76. http://dx.doi.org/10.1142/s0218539301000359.

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Generalized Poisson distributions appear as applied-research models in many fields. For example in reliability, the total amount of wear of items, the hazard rate and the total time to failure can be modeled after a Generalized Poisson distribution. Methods of Statistical Inference for such distributions have been scarce since the corresponding distribution functions come in complicated, often not closed form, expressions. In this article, we present a method for testing the goodness-of-fit to any specified member of the family of Generalized Poisson distributions. The proposed method utilizes the general form of the moment generating function of Generalized Poisson distributions. The asymptotic distribution of the test statistics is derived when the parameters of the generalizing distribution are assumed known as well as unknown. The performance of the procedures is investigated by employing real and simulated data.

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6

Mathur, S. K., i D. M. Sakate. "A new test for two-sample location problem based on empirical distribution function". Communications in Statistics - Theory and Methods 46, nr 24 (21.02.2017): 12345–55. http://dx.doi.org/10.1080/03610926.2017.1295158.

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7

Aki, Sigeo. "Some test statistics based on the martingale term of the empirical distribution function". Annals of the Institute of Statistical Mathematics 38, nr 1 (grudzień 1986): 1–21. http://dx.doi.org/10.1007/bf02482496.

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8

González-Albornoz, Pablo, i Francisco Novoa-Muñoz. "Goodness-of-Fit Test for the Bivariate Hermite Distribution". Axioms 12, nr 1 (22.12.2022): 7. http://dx.doi.org/10.3390/axioms12010007.

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This paper studies the goodness of fit test for the bivariate Hermite distribution. Specifically, we propose and study a Cramér–von Mises-type test based on the empirical probability generation function. The bootstrap can be used to consistently estimate the null distribution of the test statistics. A simulation study investigates the goodness of the bootstrap approach for finite sample sizes.

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9

Bierens, Herman J., i Li Wang. "INTEGRATED CONDITIONAL MOMENT TESTS FOR PARAMETRIC CONDITIONAL DISTRIBUTIONS". Econometric Theory 28, nr 2 (2.08.2011): 328–62. http://dx.doi.org/10.1017/s0266466611000168.

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In this paper we propose consistent integrated conditional moment tests for the validity of parametric conditional distribution models, based on the integrated squared difference between the empirical characteristic function of the actual data and the characteristic function implied by the model. To avoid numerical evaluation of the conditional characteristic function of the model distribution, a simulated integrated conditional moment test is proposed. As an empirical application we test the validity of a few common health economic count data models.

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10

Towhidi, M., i M. Salmanpour. "A New Goodness-of-Fit Test for a Distribution by the Empirical Characteristic Function". Journal of Statistical Research of Iran 2, nr 1 (1.09.2005): 1–13. http://dx.doi.org/10.18869/acadpub.jsri.2.1.1.

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11

Samar, María M., Constantino Ferro Fontán, Silvia L. Resnik, Ana M. Pacin i Marcelo D. Castillo. "Distribution of Deoxynivalenol in Wheat, Wheat Flour, Bran, and Gluten, and Variability Associated with the Test Procedure". Journal of AOAC INTERNATIONAL 86, nr 3 (1.05.2003): 551–56. http://dx.doi.org/10.1093/jaoac/86.3.551.

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Abstract Analytical data obtained on deoxynivalenol (DON) concentration in naturally contaminated wheat during processing in an industrial mill were statistically analyzed, and the distribution functions of DON concentration in lots of wheat, bran, wheat flour, and gluten were estimated. The analytical method had acceptable precision (HORRAT 0.25—0.32) for each test sample. The total variance combined sampling, sample preparation, and analytical variances were 0.188, 0.033, 0.42, and 0.0014 ppm2 for wheat, 1.93; flour, 0.99; bran, 4.68; and gluten, 0.29, respectively. The distribution function of DON contamination presented an asymmetric tail for high values of concentration in wheat grains and wheat flour; in bran it seemed to be bimodal with 2 separated peaks of different concentrations; in gluten the normal distribution function gave a reasonably good fit to empirical data. The function η(c) = –ln(–lnp), where p (c) is the cumulative distribution function was linear with c in the so-called extreme-value type I distribution and could be fitted by a cubic polynomial in c in the distributions determined for all the products. This variability and distributional information contributes to the design of better sampling plans in order to reduce the total variability and to estimate errors in the evaluation of DON concentration in lots of wheat and wheat products.

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12

Best, D. J., J. C. W. Rayner i O. Thas. "Tests of Fit for the Logarithmic Distribution". Journal of Applied Mathematics and Decision Sciences 2008 (19.03.2008): 1–8. http://dx.doi.org/10.1155/2008/463781.

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Smooth tests for the logarithmic distribution are compared with three tests: the first is a test due to Epps and is based on a probability generating function, the second is the Anderson-Darling test, and the third is due to Klar and is based on the empirical integrated distribution function. These tests all have substantially better power than the traditional Pearson-Fisher X2 test of fit for the logarithmic. These traditional chi-squared tests are the only logarithmic tests of fit commonly applied by ecologists and other scientists.

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13

Spurr, B. D., i C. D. Sinclair. "A General formula for the upper tail significance levels of empirical distribution function test statistics". Communications in Statistics - Theory and Methods 17, nr 12 (styczeń 1988): 4121–31. http://dx.doi.org/10.1080/03610928808829861.

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14

Baringhaus, L., i N. Henze. "A goodness of fit test for the Poisson distribution based on the empirical generating function". Statistics & Probability Letters 13, nr 4 (marzec 1992): 269–74. http://dx.doi.org/10.1016/0167-7152(92)90033-2.

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15

Sato, Aki Hiro. "A Method to Quantify Risks of Financial Assets: An Empirical Analysis of Japanese Security Prices". Advanced Materials Research 452-453 (styczeń 2012): 469–73. http://dx.doi.org/10.4028/www.scientific.net/amr.452-453.469.

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This study investigates unconditional distributions of daily log-returns of Japanese security prices from a comprehensive point of view. The purpose of this article is to estimate a risk distribution of stocks in terms of Value-at-Risk (VaR) in order to select low risk securities from many securities. Daily log-return time series of 1,340 Japanese companies listed on the first section of Tokyo Stock Exchange are examined during the last one decade. I develop a method to estimate VaR by both the maximum likelihood estimation procedure under a q-Gaussian assumption and analytical form of its cumulative distribution function. It is confirmed that they are fitted to q-Gaussian distributions (Student t-distributions) with Kolmogorov-Smirnov test. It is found that the complementary cumulative distribution function of VaR has a power-law tail with its characteristic exponent depending on values of the VaR percentile.

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16

dos Santos, Marcos Alex, Quirijn de Jong van Lier, Jos C. van Dam i Andre Herman Freire Bezerra. "Benchmarking test of empirical root water uptake models". Hydrology and Earth System Sciences 21, nr 1 (26.01.2017): 473–93. http://dx.doi.org/10.5194/hess-21-473-2017.

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Abstract. Detailed physical models describing root water uptake (RWU) are an important tool for the prediction of RWU and crop transpiration, but the hydraulic parameters involved are hardly ever available, making them less attractive for many studies. Empirical models are more readily used because of their simplicity and the associated lower data requirements. The purpose of this study is to evaluate the capability of some empirical models to mimic the RWU distribution under varying environmental conditions predicted from numerical simulations with a detailed physical model. A review of some empirical models used as sub-models in ecohydrological models is presented, and alternative empirical RWU models are proposed. All these empirical models are analogous to the standard Feddes model, but differ in how RWU is partitioned over depth or how the transpiration reduction function is defined. The parameters of the empirical models are determined by inverse modelling of simulated depth-dependent RWU. The performance of the empirical models and their optimized empirical parameters depends on the scenario. The standard empirical Feddes model only performs well in scenarios with low root length density R, i.e. for scenarios with low RWU compensation. For medium and high R, the Feddes RWU model cannot mimic properly the root uptake dynamics as predicted by the physical model. The Jarvis RWU model in combination with the Feddes reduction function (JMf) only provides good predictions for low and medium R scenarios. For high R, it cannot mimic the uptake patterns predicted by the physical model. Incorporating a newly proposed reduction function into the Jarvis model improved RWU predictions. Regarding the ability of the models to predict plant transpiration, all models accounting for compensation show good performance. The Akaike information criterion (AIC) indicates that the Jarvis (2010) model (JMII), with no empirical parameters to be estimated, is the best model. The proposed models are better in predicting RWU patterns similar to the physical model. The statistical indices point to them as the best alternatives for mimicking RWU predictions of the physical model.

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17

BIANCHI, SERGIO. "A NEW DISTRIBUTION-BASED TEST OF SELF-SIMILARITY". Fractals 12, nr 03 (wrzesień 2004): 331–46. http://dx.doi.org/10.1142/s0218348x04002586.

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In studying the scale invariance of an empirical time series a twofold problem arises: it is necessary to test the series for self-similarity and, once passed such a test, the goal becomes to estimate the parameter H0 of self-similarity. The estimation is therefore correct only if the sequence is truly self-similar but in general this is just assumed and not tested in advance. In this paper we suggest a solution for this problem. Given the process {X(t),t∈T}, we propose a new test based on the diameter δ of the space of the rescaled probability distribution functions of X(t). Two necessary conditions are deduced which contribute to discriminate self-similar processes and a closed formula is provided for the diameter of the fractional Brownian motion (fBm). Furthermore, by properly choosing the distance function, we reduce the measure of self-similarity to the Smirnov statistics when the one-dimensional distributions of X(t) are considered. This permits the application of the well-known two-sided test due to Kolmogorov and Smirnov in order to evaluate the statistical significance of the diameter δ, even in the case of strongly dependent sequences. As a consequence, our approach both tests the series for self-similarity and provides an estimate of the self-similarity parameter.

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18

Abul Naga, Ramses, Christopher Stapenhurst i Gaston Yalonetzky. "Asymptotic Versus Bootstrap Inference for Inequality Indices of the Cumulative Distribution Function". Econometrics 8, nr 1 (26.02.2020): 8. http://dx.doi.org/10.3390/econometrics8010008.

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We examine the performance of asymptotic inference as well as bootstrap tests for the Alphabeta and Kobus–Miłoś family of inequality indices for ordered response data. We use Monte Carlo experiments to compare the empirical size and statistical power of asymptotic inference and the Studentized bootstrap test. In a broad variety of settings, both tests are found to have similar rejection probabilities of true null hypotheses, and similar power. Nonetheless, the asymptotic test remains correctly sized in the presence of certain types of severe class imbalances exhibiting very low or very high levels of inequality, whereas the bootstrap test becomes somewhat oversized in these extreme settings.

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19

Zamanzade, Ehsan, i Mahdi Mahdizadeh. "Entropy Estimation From Ranked Set Samples With Application to Test of Fit". Revista Colombiana de Estadística 40, nr 2 (1.07.2017): 223–41. http://dx.doi.org/10.15446/rce.v40n2.58944.

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This article deals with entropy estimation using ranked set sampling (RSS). Some estimators are developed based on the empirical distribution function and its nonparametric maximum likelihood competitor. The suggested entropy estimators have smaller root mean squared errors than the other entropy estimators in the literature. The proposed estimators are then used to construct goodness of fit tests for inverse Gaussian distribution.

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20

Chlebus, Marcin. "Can Lognormal, Weibull or Gamma Distributions Improve the EWS-GARCH Value-at-Risk Forecasts?" Przegląd Statystyczny 63, nr 3 (30.09.2016): 329–50. http://dx.doi.org/10.5604/01.3001.0014.1212.

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In the study, two-step EWS-GARCH models to forecast Value-at-Risk are analysed. The following models were considered: the EWS-GARCH models with lognormal, Weibull or Gamma distributions as a distributions in a state of turbulence, and with GARCH(1,1) or GARCH(1,1) with the amendment to empirical distribution of random error models as models used in a state of tranquillity. The evaluation of the quality of the Value-at-Risk forecasts was based on the Value-at-Risk forecasts adequacy (the excess ratio, the Kupiec test, the Christoffersen test, the asymptotic test of unconditional coverage and the backtesting criteria defined by the Basel Committee) and the analysis of loss func-tions (the Lopez quadratic loss function, the Abad & Benito absolute loss function, the 3rd version of Caporin loss function and the function of excessive costs). Obtained results show that the EWS-GARCH models with lognormal, Weibull or Gamma distributions may compete with EWS-GARCH models with exponential and empirical distributions. The EWS-GARCH model with lognormal, Weibull or Gamma distributions are relatively less conservative, but using them is less expensive than using the other EWS-GARCH models.

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21

Towhidi, M., i M. Salmanpour. "A test of fit for a continuous distribution based on the empirical convex conditional mean function". Communications in Statistics - Theory and Methods 46, nr 3 (8.03.2016): 1490–505. http://dx.doi.org/10.1080/03610926.2015.1019151.

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22

Herawati, Netti, i Ibrahim A. Ahmad. "Smooth Versions of the Mann–Whitney–Wilcoxon Statistics". Axioms 11, nr 7 (21.06.2022): 300. http://dx.doi.org/10.3390/axioms11070300.

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The well-known Mann–Whitney–Wilcoxon (MWW) statistic is based on empirical distribution estimates. However, the data are often drawn from smooth populations. Therefore, the smoothness characteristic is not preserved. In addition, several authors have pointed out that empirical distribution is often an inadmissible estimate. Thus, in this work, we develop smooth versions of the MWW statistic based on smooth distribution function estimates. This approach preserves the data characteristics and allows the efficiency of the procedure to improve. In addition, our procedure is shown to be robust against a large class of dependent observations. Hence, by choosing a rectangular array of known distribution functions, our procedure allows the test to be a lot more reflective of the real data.

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23

CAPASSO, MARCO, LUCIA ALESSI, MATTEO BARIGOZZI i GIORGIO FAGIOLO. "ON APPROXIMATING THE DISTRIBUTIONS OF GOODNESS-OF-FIT TEST STATISTICS BASED ON THE EMPIRICAL DISTRIBUTION FUNCTION: THE CASE OF UNKNOWN PARAMETERS". Advances in Complex Systems 12, nr 02 (kwiecień 2009): 157–67. http://dx.doi.org/10.1142/s0219525909002131.

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This paper discusses some problems possibly arising when approximating via Monte-Carlo simulations the distributions of goodness-of-fit test statistics based on the empirical distribution function. We argue that failing to re-estimate unknown parameters on each simulated Monte-Carlo sample — and thus avoiding to employ this information to build the test statistic — may lead to wrong, overly-conservative. Furthermore, we present some simple examples suggesting that the impact of this possible mistake may turn out to be dramatic and does not vanish as the sample size increases.

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24

Fakoor, Vahid, Masoud Ajami, Seyed Mahdi Amir Jahanshahi i Ali Shariati. "A Density-Based Empirical Likelihood Ratio Approach for Goodness-of-fit Tests in Decreasing Densities". Statistics, Optimization & Information Computing 8, nr 1 (17.02.2020): 66–79. http://dx.doi.org/10.19139/soic-2310-5070-707.

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In this paper, we propose a test for the null hypothesis that a decreasing density function belongs to a givenparametric family of distribution functions against the non-parametric alternative. This method, which is based on an empirical likelihood (EL) ratio statistic, is similar to the test introduced by Vexler and Gurevich [23]. The consistency of the test statistic proposed is derived under the null and alternative hypotheses. A simulation study is conducted to inspect the power of the proposed test under various decreasing alternatives. In each scenario, the critical region of the test is obtained using a Monte Carlo technique. The applicability of the proposed test in practice is demonstrated through a few real data examples.

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Vargas, Eugenia Azevedo, Thomas B. Whitaker, Eliene Alves dos Santos, Andrew B. Slate, Francisco B. Lima i Regina C. A. Franca. "Testing Green Coffee for Ochratoxin A, Part II: Observed Distribution of Ochratoxin A Test Results". Journal of AOAC INTERNATIONAL 88, nr 3 (1.05.2005): 780–87. http://dx.doi.org/10.1093/jaoac/88.3.780.

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Abstract The suitability of 4 theoretical distributions (normal, lognormal, negative binomial, and gamma) to predict the observed distribution of ochratoxin A (OTA) in green coffee was investigated. One symmetrical and 3 positively skewed theoretical distributions were each fitted to 25 empirical distributions of OTA test results for green coffee beans. Parameters of each theoretical distribution were calculated by using Methods of Moments. The 3 skewed theoretical distributions provided acceptable fits to each of the 25 observed distributions. Because of its simplicity, the lognormal distribution was selected to model OTA test results for green coffee. Using variance equations determined in previous studies, mathematical expressions were developed to calculate the parameters of the log normal distribution for a given OTA lot concentration and test procedure. Observed acceptance probabilities were compared to an operating characteristic curve predicted from the lognormal distribution, and all 25 observed acceptance probabilities were found to lie within the 95% confidence band associated with the predicted operating characteristic curve. The parameters of compound gamma distribution were used to calculate the fraction of OTA contamination beans within a contaminated lot. The percent-contaminated beans were a function of the lot concentration and increased with lot concentration. At a lot concentration of 5 μg/kg, approximately 6 beans per 10 000 beans are contaminated.

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Contreras-Reyes, Javier E. "An Asymptotic Test for Bimodality Using The Kullback–Leibler Divergence". Symmetry 12, nr 6 (16.06.2020): 1013. http://dx.doi.org/10.3390/sym12061013.

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Detecting bimodality of a frequency distribution is of considerable interest in several fields. Classical inferential methods for detecting bimodality focused in third and fourth moments through the kurtosis measure. Nonparametric approach-based asymptotic tests (DIPtest) for comparing the empirical distribution function with a unimodal one are also available. The latter point drives this paper, by considering a parametric approach using the bimodal skew-symmetric normal distribution. This general class captures bimodality, asymmetry and excess of kurtosis in data sets. The Kullback–Leibler divergence is considered to obtain the statistic’s test. Some comparisons with DIPtest, simulations, and the study of sea surface temperature data illustrate the usefulness of proposed methodology.

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Kuleshov, E. L., K. A. Petrov i T. S. Kirillova. "GOODNESS-OF-FIT TEST ON THE BASIS OF THE CONFIDENCE INTERVALS OF THE EMPIRICAL PROBABILITY DISTRIBUTION FUNCTION". Informatika i sistemy upravleniya, nr 52 (2017): 72–84. http://dx.doi.org/10.22250/isu.2017.52.72-84.

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van der Linden, Wim J., i Leonardo Sotaridona. "Detecting Answer Copying When the Regular Response Process Follows a Known Response Model". Journal of Educational and Behavioral Statistics 31, nr 3 (wrzesień 2006): 283–304. http://dx.doi.org/10.3102/10769986031003283.

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A statistical test for detecting answer copying on multiple-choice items is presented. The test is based on the exact null distribution of the number of random matches between two test takers under the assumption that the response process follows a known response model. The null distribution can easily be generalized to the family of distributions of the number of random matches under the alternative hypothesis of answer copying. It is shown how this information can be used to calculate such features as the maximum, minimum, and expected values of the power function of the test. For the case of the nominal response model, the test is an alternative to the one based on statistic ω. The differences between the two tests are discussed and illustrated using empirical results.

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Lebedev, Valery, Konstantin Lebedev i Tatyana Tyupikova. "Application of parabolic spline for population income distributions analysis". System Analysis in Science and Education, nr 4 (2019) (2019): 24–31. http://dx.doi.org/10.37005/2071-9612-2019-4-24-31.

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The aim of the study is an empirical test of the hypothesis about the possibility of using the lognormal function as an adequate model of the distribution of the population by income. The method of spline functions is used as the main research tool. The values of the free parameters of the parabolic spline were determined from the solution of the problem of minimizing the integral smoothness of the distribution function under the condition of its monotonic increase. As the information base of the study, statistical data on the distribution of wages of employees of organizations of the Russian Federation in 2019 were used. This work was supported by the Russian Foundation for Basic Research, grant No. 19-010-000921.

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Ba, Amadou Diadie, El Hadj Deme, Cheikh Tidiane Seck i Gane Samb Lo. "Consistency Bands for the Mean Excess Function and Application to Graphical Goodness-of-fit Test for Financial Data". Journal of Mathematics Research 8, nr 1 (24.01.2016): 42. http://dx.doi.org/10.5539/jmr.v8n1p42.

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<p>In this paper, we use the modern setting of functional empirical processes and recent techniques on uniform estimation for non parametric objects to derive consistency bands for the mean excess function in the i.i.d. case. We apply our results for modelling Dow Jones data to see how good the Generalized hyperbolic distribution fits monthly data.</p>

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31

Nad, Alona, i Marian Brożek. "Application of Three-Parameter Distribution to Approximate the Particle Size Distribution Function of Comminution Products of Dolomitic Type of Copper Ore". Archives of Mining Sciences 62, nr 2 (27.06.2017): 411–22. http://dx.doi.org/10.1515/amsc-2017-0031.

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AbstractThe paper presents the results of analyze the particle size distribution function of comminution products of dolomitic type of copper ore. The breakage tests for single irregular particles were performed with using a hydraulic press device. The authors prepared five particle size fractions of each material, within ranges: 16-18 mm, 18-20 mm, 20-25 mm, 25-31,5 mm and 31-45 mm. The particle size distribution function of single-particle breakage test was calculated separately for each size fraction. In addition, the cumulative particle size distribution function for five particle size fractions was presented. In theoretical part the study of applied functions of particle size distribution for comminution a set of particles and models of crushing single particles was performed. In that paper the curves of the particle size distribution were approximated by the three-parameter function, which parameters depend on the particle strength and material type. For conformity assessment the model distribution function to the empirical distribution function a residual deviation and non-linear correlation coefficient were calculated. The three-parameter function approximating agrees well with the particle size distribution obtained from experimental data. The dependence of the parameters of a particle size distribution function on the dolomite particle strength was presented. The results indicate the identity of single particle grinding mechanism by slow compression of irregular particles of dolomitic type of copper ore, regardless of the initial particle size.

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Cianciara, Aleksander. "Results of the Verification of the Statistical Distribution Model of Microseismicity Emission Characteristics". Archives of Mining Sciences 61, nr 3 (1.09.2016): 489–96. http://dx.doi.org/10.1515/amsc-2016-0035.

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Abstract The paper presents the results of research aimed at verifying the hypothesis that the Weibull distribution is an appropriate statistical distribution model of microseismicity emission characteristics, namely: energy of phenomena and inter-event time. It is understood that the emission under consideration is induced by the natural rock mass fracturing. Because the recorded emission contain noise, therefore, it is subjected to an appropriate filtering. The study has been conducted using the method of statistical verification of null hypothesis that the Weibull distribution fits the empirical cumulative distribution function. As the model describing the cumulative distribution function is given in an analytical form, its verification may be performed using the Kolmogorov-Smirnov goodness-of-fit test. Interpretations by means of probabilistic methods require specifying the correct model describing the statistical distribution of data. Because in these methods measurement data are not used directly, but their statistical distributions, e.g., in the method based on the hazard analysis, or in that that uses maximum value statistics.

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33

Broda, Simon A. "Testing for individual sphericity in heterogeneous panels". Biometrika 106, nr 3 (13.05.2019): 740–47. http://dx.doi.org/10.1093/biomet/asz018.

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Summary This manuscript considers locally best invariant tests for sphericity in heterogeneous panels. A new integral representation for the characteristic function of the test statistic under the null is presented, along with an algorithm for inverting it to obtain the distribution function. A saddlepoint approximation to the null distribution addresses the need to quickly compute approximate $p$-values in empirical work. The approximation shows substantial improvements over the normal approximation when the cross-sectional dimension is small.

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Barbosa, Josino José, Tiago Martins Pereira i Fernando Luiz Pereira de Oliveira. "Uma proposta para identificação de outliers multivariados". Ciência e Natura 40 (6.07.2018): 40. http://dx.doi.org/10.5902/2179460x29535.

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In the last years several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. For instance, Ghitany et al. (2013) proposed a new generalization of the Lindley distribution, called power Lindley distribution, whereas Sharma et al. (2015a) proposed the inverse Lindley distribution. From these two generalizations Barco et al. (2017) studied the inverse power Lindley distribution, also called by Sharma et al. (2015b) as generalized inverse Lindley distribution. Considering the inverse power Lindley distribution, in this paper is evaluate the performance, through Monte Carlo simulations, with respect to the bias and consistency of nine different methods of estimations (the maximum likelihood method and eight others based on the distance between the empirical and theoretical cumulative distribution function). The numerical results showed a better performance of the estimation method based on the Anderson-Darling test statistic. This conclusion is also observed in the analysis of two real data sets.

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Espey, Brian R. "Empirical Modelling of Public Lighting Emission Functions". Remote Sensing 13, nr 19 (24.09.2021): 3827. http://dx.doi.org/10.3390/rs13193827.

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Study of light at night has increased in recent decades due to the recognition of its impact on the environment, potential health concerns, as well as both the financial and carbon cost of energy waste. The advent of more extensive and improved ground-based measurements together with quantifiable satellite data has revolutionised the field, and provided data to test improved theoretical models. However, “closing the loop” and finding a detailed connection between these measurements requires knowledge of the “city emission function”, the angular distribution of upwelling radiation with zenith distance. Simplified analytical functions have been superseded by more complex models involving statistical approximation of emission sources and obstructions and inversion techniques now permit the estimation of emission functions from the observed sky brightness measurements. In this paper, we present an efficient GIS-based method to model public lighting using real-world photometric data and high-resolution digital elevation maps of obstructions such as buildings and trees at a 1 m scale. We discuss the results of this work for a sample of Irish towns as well as a city area. We also compare our results to previous emission functions as well as to observed asymmetries in emission detected by satellites such as SUOMI VIIRS.

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Wang, Zifeng, Hong Zhu, Zhenhua Dong, Xiuqiang He i Shao-Lun Huang. "Less Is Better: Unweighted Data Subsampling via Influence Function". Proceedings of the AAAI Conference on Artificial Intelligence 34, nr 04 (3.04.2020): 6340–47. http://dx.doi.org/10.1609/aaai.v34i04.6103.

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In the time of Big Data, training complex models on large-scale data sets is challenging, making it appealing to reduce data volume for saving computation resources by subsampling. Most previous works in subsampling are weighted methods designed to help the performance of subset-model approach the full-set-model, hence the weighted methods have no chance to acquire a subset-model that is better than the full-set-model. However, we question that how can we achieve better model with less data? In this work, we propose a novel Unweighted Influence Data Subsampling (UIDS) method, and prove that the subset-model acquired through our method can outperform the full-set-model. Besides, we show that overly confident on a given test set for sampling is common in Influence-based subsampling methods, which can eventually cause our subset-model's failure in out-of-sample test. To mitigate it, we develop a probabilistic sampling scheme to control the worst-case risk over all distributions close to the empirical distribution. The experiment results demonstrate our methods superiority over existed subsampling methods in diverse tasks, such as text classification, image classification, click-through prediction, etc.

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Huber, Adrian E. G., Jithendar Anumula i Shih-Chii Liu. "Optimal Sampling of Parametric Families: Implications for Machine Learning". Neural Computation 32, nr 1 (styczeń 2020): 261–79. http://dx.doi.org/10.1162/neco_a_01251.

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It is well known in machine learning that models trained on a training set generated by a probability distribution function perform far worse on test sets generated by a different probability distribution function. In the limit, it is feasible that a continuum of probability distribution functions might have generated the observed test set data; a desirable property of a learned model in that case is its ability to describe most of the probability distribution functions from the continuum equally well. This requirement naturally leads to sampling methods from the continuum of probability distribution functions that lead to the construction of optimal training sets. We study the sequential prediction of Ornstein-Uhlenbeck processes that form a parametric family. We find empirically that a simple deep network trained on optimally constructed training sets using the methods described in this letter can be robust to changes in the test set distribution.

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38

Goerg, Sebastian J., i Johannes Kaiser. "Nonparametric Testing of Distributions—the Epps–Singleton Two-Sample Test using the Empirical Characteristic Function". Stata Journal: Promoting communications on statistics and Stata 9, nr 3 (wrzesień 2009): 454–65. http://dx.doi.org/10.1177/1536867x0900900307.

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Ciupak, Maurycy, Bogdan Ozga-Zieliński, Tamara Tokarczyk i Jan Adamowski. "A Probabilistic Model for Maximum Rainfall Frequency Analysis". Water 13, nr 19 (28.09.2021): 2688. http://dx.doi.org/10.3390/w13192688.

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As determining the probability of the exceedance of maximum precipitation over a specified duration is critical to hydrotechnical design, particularly in the context of climate change, a model was developed to perform a frequency analysis of maximum precipitation of a specified duration. The PMAXΤP model (Precipitation MAXimum Time (duration) Probability) harbors a pair of computational modules fulfilling different roles: (i) statistical analysis of precipitation series, and (ii) estimation of maximum precipitation for a specified duration and its probability of exceedance. The input data consist of homogeneous 30-element series of precipitation values for 16 different durations: 5, 10, 15, 30, 45, 60, 90, 120, 180, 360, 720, 1080, 1440, 2160, 2880, and 4320 min, obtained through Annual Maximum Precipitation (AMP) and Peaks-Over-Threshold (POT) approaches. The statistical analysis of the precipitation series includes: (i) detecting outliers using the Grubbs-Beck test; (ii) checking for the random variable’s independence using the Wald-Wolfowitz test and the Anderson serial correlation coefficient test; (iii) checking the random variable’s stationarity using nonparametric tests, e.g., the Kruskal-Wallis test and Spearman rank correlation coefficient test for trends of mean and variance; (iv) identifying the trend of the random variables using correlation and regression analysis, including an evaluation of the form of the trend function; and (v) checking for the internal correlation of the random variables using the Anderson autocorrelation coefficient test. To estimate maximum precipitations of a specified duration and with a specified probability of exceedance, three-parameter theoretical probability distributions were used: a shifted gamma distribution (Pearson type III), a log-normal distribution, a Weibull distribution (Fisher-Tippett type III), a log-gamma distribution, as well as a two-parameter Gumbel distribution. The best distribution was selected by: (i) maximum likelihood estimation of parameters; (ii) tests of the hypothesis of goodness of fit of the theoretical probability distribution function with the empirical distribution using Pearson’s χ2 test; (iii) selection of the best-fitting function within each type according to the criterion of minimum Kolmogorov distance; (iv) selection of the most credible probability distribution function from the set of various types of best-fitting functions according to the Akaike information criterion; and (v) verification of the most credible function using single-dimensional tests of goodness of fit: the Kolmogorov-Smirnov test, the Anderson-Darling test, the Liao-Shimokawa test, and Kuiper’s test. The PMAXTP model was tested on data from two meteorological stations in northern Poland (Chojnice and Bialystok) drawn from a digital database of high-resolution precipitation records for the period of 1986 to 2015, available for 100 stations in Poland (i.e., the Polish Atlas of Rainfall Intensities (PANDa)). Values of maximum precipitation with a specified probability of exceedance obtained from the PMAXTP model were compared with values obtained from the probabilistic Bogdanowicz-Stachý model. The comparative analysis was based on the standard error of fit, graphs of the density function for the probability of exceedance, and estimated quantile errors. The errors of fit were lower for the PMAXTP compared to the Bogdanowicz-Stachý model. For both stations, the smallest errors were obtained for the quantiles determined on the basis of maximum precipitation POT using PMAXTP.

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Kim, Wonik. "Institutional Origins of Unemployment Compensation: An Empirical Analysis of the Developing World, 1946–2000". Business and Politics 8, nr 1 (kwiecień 2006): 1–28. http://dx.doi.org/10.2202/1469-3569.1142.

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Why do some countries institutionalize a social program compensating the unemployed while others do not? My main argument is that the choice to have an unemployment insurance program is a function of 1) the distribution of unemployment risks within a country and 2) political processes through which demands for insurance are realized. The distribution of industrial-specific risks and workers' employment status are the driving force in shaping workers' demands. In developing countries, these demands are more likely to be realized under democratic regimes. An event history model for 102 developing countries from 1946 to 2000 is used to test the arguments.

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Mittelhammer, Ron, George Judge i Miguel Henry. "An Entropy-Based Approach for Nonparametrically Testing Simple Probability Distribution Hypotheses". Econometrics 10, nr 1 (14.01.2022): 5. http://dx.doi.org/10.3390/econometrics10010005.

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In this paper, we introduce a flexible and widely applicable nonparametric entropy-based testing procedure that can be used to assess the validity of simple hypotheses about a specific parametric population distribution. The testing methodology relies on the characteristic function of the population probability distribution being tested and is attractive in that, regardless of the null hypothesis being tested, it provides a unified framework for conducting such tests. The testing procedure is also computationally tractable and relatively straightforward to implement. In contrast to some alternative test statistics, the proposed entropy test is free from user-specified kernel and bandwidth choices, idiosyncratic and complex regularity conditions, and/or choices of evaluation grids. Several simulation exercises were performed to document the empirical performance of our proposed test, including a regression example that is illustrative of how, in some contexts, the approach can be applied to composite hypothesis-testing situations via data transformations. Overall, the testing procedure exhibits notable promise, exhibiting appreciable increasing power as sample size increases for a number of alternative distributions when contrasted with hypothesized null distributions. Possible general extensions of the approach to composite hypothesis-testing contexts, and directions for future work are also discussed.

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Ma, Bin, Min Luo, Zhi Chu Chen i Li Xin Cao. "Reliability Analysis of the Home and Abroad CNC Equipment Used in Automobile Parts Industry". Applied Mechanics and Materials 651-653 (wrzesień 2014): 802–7. http://dx.doi.org/10.4028/www.scientific.net/amm.651-653.802.

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Through analyzing fault information of the home and abroad CNC equipment used in the same auto parts production, the fault data fitting were implemented in this paper. Assuming time between failure probability density function and the empirical distribution function follow the Weibull distribution, A reliability statistical model was built using the least squares method and a linear parameter distribution model regression method. The linear correlation test and the Weibull distribution fault interval obtained show the fact that both the home and abroad equipment are subject to the two parameter Weibull distribution, and after calculating the three indexes of reliability assessment, a conclusion can be made that the reliability of domestic equipment in the study is slightly lower than that of foreign equipment.

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Antonelli, Maria Alessandra, i Valeria De Bonis. "Strategic Welfare Policies with Migration: A Theoretical Model and Empirical Evidence". Review of Economics 72, nr 1 (1.04.2021): 29–50. http://dx.doi.org/10.1515/roe-2020-0033.

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Abstract We test the welfare magnet hypothesis for Europe. We modify the existing theoretical frameworks assuming that: (a) welfare services, intended as the output of welfare expenditure, not the poor’s income or social expenditure, enter the median voter’s utility function; (b) preferences depend on the position of the median voter in the income distribution; and (c) the total amount of welfare services provided may differ from the amount needed to finance them, because of inefficiencies in the transfer process. We then test the welfare magnet hypothesis for 22 European countries by estimating a reaction function corresponding to the generic form adopted by the literature, but using the variables inspired by the model. We find evidence of a positive strategic interaction among countries, which suggests a downward bias in the choice of the protection level because of welfare competition. The level of social protection also positively depends on GDP, the redistributive attitudes of residents and their weight in the population, vis-à-vis the migrants’ share, and the efficiency of social expenditure.

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Avdović, Atif, i Vesna Jevremović. "Quantile-Zone Based Approach to Normality Testing". Mathematics 10, nr 11 (26.05.2022): 1828. http://dx.doi.org/10.3390/math10111828.

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Normality testing remains an important issue for researchers, despite many solutions that have been published and in use for a long time. There is a need for testing normality in many areas of research and application, among them in Quality control, or more precisely, in the investigation of Shewhart-type control charts. We modified some of our previous results concerning control charts by using the empirical distribution function, proper choice of quantiles and a zone function that quantifies the discrepancy from a normal distribution. That was our approach in constructing a new normality test that we present in this paper. Our results show that our test is more powerful than any other known normality test, even in the case of alternatives with small departures from normality and for small sample sizes. Additionally, many test statistics are sensitive to outliers when testing normality, but that is not the case with our test statistic. We provide a detailed distribution of the test statistic for the presented test and comparable power analysis with highly illustrative graphics. The discussion covers both the cases for known and for estimated parameters.

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Lee, Sokbae, Kyungchul Song i Yoon-Jae Whang. "TESTING FOR A GENERAL CLASS OF FUNCTIONAL INEQUALITIES". Econometric Theory 34, nr 5 (1.12.2017): 1018–64. http://dx.doi.org/10.1017/s0266466617000329.

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In this article, we propose a general method for testing inequality restrictions on nonparametric functions. Our framework includes many nonparametric testing problems in a unified framework, with a number of possible applications in auction models, game theoretic models, wage inequality, and revealed preferences. Our test involves a one-sided version ofLpfunctionals of kernel-type estimators (1 ≤p < ∞) and is easy to implement in general, mainly due to its recourse to the bootstrap method. The bootstrap procedure is based on the nonparametric bootstrap applied to kernel-based test statistics, with an option of estimating “contact sets.” We provide regularity conditions under which the bootstrap test is asymptotically valid uniformly over a large class of distributions, including cases where the limiting distribution of the test statistic is degenerate. Our bootstrap test is shown to exhibit good power properties in Monte Carlo experiments, and we provide a general form of the local power function. As an illustration, we consider testing implications from auction theory, provide primitive conditions for our test, and demonstrate its usefulness by applying our test to real data. We supplement this example with the second empirical illustration in the context of wage inequality.

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Soukarieh, Inass, i Salim Bouzebda. "Exchangeably Weighted Bootstraps of General Markov U-Process". Mathematics 10, nr 20 (12.10.2022): 3745. http://dx.doi.org/10.3390/math10203745.

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We explore an exchangeably weighted bootstrap of the general function-indexed empirical U-processes in the Markov setting, which is a natural higher-order generalization of the weighted bootstrap empirical processes. As a result of our findings, a considerable variety of bootstrap resampling strategies arise. This paper aims to provide theoretical justifications for the exchangeably weighted bootstrap consistency in the Markov setup. General structural conditions on the classes of functions (possibly unbounded) and the underlying distributions are required to establish our results. This paper provides the first general theoretical study of the bootstrap of the empirical U-processes in the Markov setting. Potential applications include the symmetry test, Kendall’s tau and the test of independence.

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Valeinis, Janis, Edmunds Cers i Juris Cielens. "TWO‐SAMPLE PROBLEMS IN STATISTICAL DATA MODELLING". Mathematical Modelling and Analysis 15, nr 1 (15.02.2010): 137–51. http://dx.doi.org/10.3846/1392-6292.2010.15.137-151.

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A common problem in mathematical statistics is to check whether two samples differ from each other. From modelling point of view it is possible to make a statistical test for the equality of two means or alternatively two distribution functions. The second approach allows to represent the two‐sample test graphically. This can be done by adding simultaneous confidence bands to the probability‐probability (P — P) or quantile‐quantile (Q — Q) plots. In this paper we compare empirically the accuracy of the classical two‐sample t‐test, empirical likelihood method and several bootstrap methods. For a real data example both Q — Q and P — P plots with simultaneous confidence bands have been plotted using the smoothed empirical likelihood and smoothed bootstrap methods.

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Guo, Xu, Gao-Rong Li, Michael McAleer i Wing-Keung Wong. "Specification Testing of Production in a Stochastic Frontier Model". Sustainability 10, nr 9 (30.08.2018): 3082. http://dx.doi.org/10.3390/su10093082.

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Parametric production frontier functions are frequently used in stochastic frontier models, but there do not seem to be any empirical test statistics for the plausibility of this application. In this paper, we develop procedures to test whether or not the parametric production frontier functions are suitable. Toward this aim, we developed two test statistics based on local smoothing and an empirical process, respectively. Residual-based wild bootstrap versions of these two test statistics are also suggested. The distributions of technical inefficiency and the noise term are not specified, which allows specification testing of the production frontier function even under heteroscedasticity. Simulation studies and a real data example are presented to examine the finite sample sizes and powers of the test statistics. The theory developed in this paper is useful for production managers in their decisions on production.

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Meintanis, Simos G. "A Kolmogorov–Smirnov type test for skew normal distributions based on the empirical moment generating function". Journal of Statistical Planning and Inference 137, nr 8 (sierpień 2007): 2681–88. http://dx.doi.org/10.1016/j.jspi.2006.04.012.

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Xi Chen, Song, i Jiti Gao. "SIMULTANEOUS SPECIFICATION TESTING OF MEAN AND VARIANCE STRUCTURES IN NONLINEAR TIME SERIES REGRESSION". Econometric Theory 27, nr 4 (3.03.2011): 792–843. http://dx.doi.org/10.1017/s0266466610000502.

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This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the variance components of the goodness-of-fit measure. To reduce the dependence of the test on a single pair of smoothing bandwidths, we construct an adaptive test by maximizing a standardized version of the empirical likelihood test statistic over a set of smoothing bandwidths. The test procedure is based on a bootstrap calibration to the distribution of the empirical likelihood test statistic. We demonstrate that the empirical likelihood test is able to distinguish local alternatives that are different from the null hypothesis at an optimal rate.

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