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Статті в журналах з теми "Statistica bivariata"

Автор: Grafiati

Опубліковано: 10 березня 2023

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1

Sinčić, Marko, Sanja Bernat Gazibara, Martin Krkač, and Snježana Mihalić Arbanas. "Landslide susceptibility assessment of the City of Karlovac using the bivariate statistical analysis." Rudarsko-geološko-naftni zbornik 38, no. 2 (2022): 149–70. http://dx.doi.org/10.17794/rgn.2022.2.13.

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A preliminary landslide susceptibility analysis on a regional scale of 1:100 000 using bivariate statistics was conducted for the City of Karlovac. The City administration compiled landslide inventory used in the analysis based on recorded landslides from 2014 to 2019 that caused significant damage to buildings or infrastructures. Analyses included 17 geofactors relevant to landslide occurrence and classified them into four groups: geomorphological (elevation, slope gradient, slope orientation, terrain curvature, terrain roughness), geological (lithology-rock type, proximity to geological contacts, proximity to faults), hydrological (proximity to drainage network, proximity to springs, proximity to temporary, permanent and to all streams, topographic wetness) and anthropogenic (proximity to traffic infrastructure, land cover using two classifications). Five scenarios were defined using a different combination of geofactors weighted by the Weights-of-Evidence (WoE) method, resulting in five different landslide susceptibility maps. The best landslide susceptibility map was selected upon the results of a ROC curve analysis, which was used to obtain success and prediction rates of each scenario. The novelty in the presented research is that a limited amount of thematic data and an incomplete landslide inventory map allows for the production of a preliminary landslide susceptibility map for usage in spatial planning. Also, this study provides a discussion regarding the used method, geofactors, defined scenarios and reliability of the results. The final preliminary landslide susceptibility map was derived using ten geofactors, which satisfied the pairwise CI test, and it is classified in four zones: low landslide susceptibility (57.05% of the area), medium landslide susceptibility (20.63% of the area), high landslide susceptibility (13.28% of the area), and very high landslide susceptibility (9.03% of the area), and has a success rate of 94% and a prediction rate of 93% making it a highly accurate source of preliminary information for the study area.

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2

Fiori, Simone. "Neural Systems with Numerically Matched Input-Output Statistic: Isotonic Bivariate Statistical Modeling." Computational Intelligence and Neuroscience 2007 (2007): 1–23. http://dx.doi.org/10.1155/2007/71859.

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Bivariate statistical modeling from incomplete data is a useful statistical tool that allows to discover the model underlying two data sets when the data in the two sets do not correspond in size nor in ordering. Such situation may occur when the sizes of the two data sets do not match (i.e., there are holes in the data) or when the data sets have been acquired independently. Also, statistical modeling is useful when the amount of available data is enough to show relevant statistical features of the phenomenon underlying the data. We propose to tackle the problem of statistical modeling via a neural (nonlinear) system that is able to match its input-output statistic to the statistic of the available data sets. A key point of the new implementation proposed here is that it is based on look-up-table (LUT) neural systems, which guarantee a computationally advantageous way of implementing neural systems. A number of numerical experiments, performed on both synthetic and real-world data sets, illustrate the features of the proposed modeling procedure.

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3

Chen, Zhenmin, and Tieyong Hu. "Statistical Test for Bivariate Uniformity." Advances in Statistics 2014 (October 19, 2014): 1–6. http://dx.doi.org/10.1155/2014/740831.

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The purpose of the multidimension uniformity test is to check whether the underlying probability distribution of a multidimensional population differs from the multidimensional uniform distribution. The multidimensional uniformity test has applications in various fields such as biology, astronomy, and computer science. Such a test, however, has received less attention in the literature compared with the univariate case. A new test statistic for checking multidimensional uniformity is proposed in this paper. Some important properties of the proposed test statistic are discussed. As a special case, the bivariate statistic test is discussed in detail in this paper. The Monte Carlo simulation is used to compare the power of the newly proposed test with the distance-to-boundary test, which is a recently published statistical test for multidimensional uniformity. It has been shown that the test proposed in this paper is more powerful than the distance-to-boundary test in some cases.

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4

de Bairros, Thiago, Pedro Pereira, Rausley de Souza, and Michel Yacoub. "Bivariate Complex $\alpha$-$\mu$ Statistics." IEEE Transactions on Vehicular Technology 71, no. 3 (March 2022): 3276–80. http://dx.doi.org/10.1109/tvt.2022.3141232.

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5

Sari, Meylita, Sutikno, and Purhadi. "Parameter estimation and hypothesis testing of geographically and temporally weighted bivariate Poisson inverse Gaussian regression model." IOP Conference Series: Earth and Environmental Science 880, no. 1 (October 1, 2021): 012045. http://dx.doi.org/10.1088/1755-1315/880/1/012045.

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Abstract One of the appropriate methods used to model count data response and its corresponding predictors is Poisson regression. Poisson regression strictly assumes that the mean and variance of response variables should be equal (equidispersion). Nonetheless, some cases of the count data unsatisfied this assumption because variance can be larger than mean (over-dispersion). If overdispersion is violated, causing the underestimate standard error. Furthermore, this will lead to incorrect conclusions in the statistical test. Thus, a suitable method for modelling this kind of data needs to develop. One alternative model to outcome the overdispersion issue in bivariate response variable is the Bivariate Poisson Inverse Gaussian Regression (BPIGR) model. The BPIGR model can produce a global model for all locations. On the other hand, each location and time have different geographic conditions, social, cultural, and economical so that Geographically and Temporally Bivariate Poisson Inverse Gaussian Regression (GTWBPIGR)) is needed. The weighting function spatial-temporal in GTWBPIGR generates a different local model for each period. GTWBPIGR model solves the overdispersion case and generates global models for each period and location. The parameter estimation of the GTWBPIGR model uses the Maximum Likelihood Estimation (MLE) method, followed by Newton Raphson iteration. Meanwhile, the test statistics on the hypothesis testing is simultaneously testing of the GTWBPIGR model is obtained with the Maximum Likelihood Ratio Test (MLRT) approach, using n large samples of the statistical test is chi-square distribution. Moreover, the test statistics for partially testing used the Z-test statistic.

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6

Abusev, R. A., and N. V. Kolegova. "On quadratic errors of statistical estimators of distributions of sufficient statistics of bivariate exponential distributions." Journal of Mathematical Sciences 126, no. 1 (March 2005): 1017–23. http://dx.doi.org/10.1007/s10958-005-0013-6.

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7

Purhadi, Purhadi, and M. Fathurahman. "A Logit Model for Bivariate Binary Responses." Symmetry 13, no. 2 (February 16, 2021): 326. http://dx.doi.org/10.3390/sym13020326.

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This article provides a bivariate binary logit model and statistical inference procedures for parameter estimation and hypothesis testing. The bivariate binary logit (BBL) model is an extension of the binary logit model that has two correlated binary responses. The BBL model responses were formed using a 2 × 2 contingency table, which follows a multinomial distribution. The maximum likelihood and Berndt–Hall–Hall–Hausman (BHHH) methods were used to obtain the BBL model. Hypothesis testing of the BBL model contains the simultaneous test and the partial test. The test statistics of the simultaneous test and the partial test were determined using the maximum likelihood ratio test method. The likelihood ratio statistics of the simultaneous test and the partial test were approximately asymptotically chi-square distributed with 3p degrees of freedom. The BBL model was applied to a real dataset, and the BBL model with the single covariate was better than the BBL model with multiple covariates.

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8

Packard, Gary C., Geoffrey F. Birchard, and Thomas J. Boardman. "Fitting statistical models in bivariate allometry." Biological Reviews 86, no. 3 (October 5, 2010): 549–63. http://dx.doi.org/10.1111/j.1469-185x.2010.00160.x.

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9

Barakat, H. M. "On Moments of Bivariate Order Statistics." Annals of the Institute of Statistical Mathematics 51, no. 2 (June 1999): 351–58. http://dx.doi.org/10.1023/a:1003818410698.

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10

Falk, Michael, and Florian Wisheckel. "Asymptotic independence of bivariate order statistics." Statistics & Probability Letters 125 (June 2017): 91–98. http://dx.doi.org/10.1016/j.spl.2017.01.020.

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11

Boland, Philip J., Myles Hollander, Kumar Joag-Dev, and Subhash Kochar. "Bivariate Dependence Properties of Order Statistics." Journal of Multivariate Analysis 56, no. 1 (January 1996): 75–89. http://dx.doi.org/10.1006/jmva.1996.0005.

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12

Kota, V. K. B., and V. Potbhare. "Bivariate distributions in statistical spectroscopy studies." Zeitschrift f�r Physik A Atoms and Nuclei 322, no. 1 (March 1985): 129–36. http://dx.doi.org/10.1007/bf01412025.

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13

Wang, Suojin. "Saddlepoint approximations for bivariate distributions." Journal of Applied Probability 27, no. 3 (September 1990): 586–97. http://dx.doi.org/10.2307/3214543.

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A saddlepoint approximation is derived for the cumulative distribution function of the sample mean of n independent bivariate random vectors. The derivations use Lugannani and Rice's saddlepoint formula and the standard bivariated normal distribution function. The separate versions of the approximation for the discrete cases are also given. A Monte Carlo study shows that the new approximation is very accurate.

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14

Reyad, Hesham, and Soha Othman. "Exploring Some Statistical Properties of the Concomitants of Upper Record Statistics for Bivariate Pseudo-Rayleigh Distribution." Asian Research Journal of Mathematics 7, no. 4 (December 13, 2017): 1–8. http://dx.doi.org/10.9734/arjom/2017/38546.

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15

Hamedani, G. G., and Hans Volkmer. "Weak convergence of bivariate sequence to bivariate normal." Communications in Statistics - Theory and Methods 46, no. 3 (March 3, 2016): 1337–41. http://dx.doi.org/10.1080/03610926.2015.1019141.

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16

Li, D., N. H. Chan, and L. Peng. "EMPIRICAL LIKELIHOOD TEST FOR CAUSALITY OF BIVARIATE AR(1) PROCESSES." Econometric Theory 30, no. 2 (October 10, 2013): 357–71. http://dx.doi.org/10.1017/s0266466613000339.

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Анотація:

Testing for causality is of critical importance for many econometric applications. For bivariate AR(1) processes, the limit distributions of causality tests based on least squares estimation depend on the presence of nonstationary processes. When nonstationary processes are present, the limit distributions of such tests are usually very complicated, and the full-sample bootstrap method becomes inconsistent as pointed out in Choi (2005, Statistics and Probability Letters 75, 39–48). In this paper, a profile empirical likelihood method is proposed to test for causality. The proposed test statistic is robust against the presence of nonstationary processes in the sense that one does not have to determine the existence of nonstationary processes a priori. Simulation studies confirm that the proposed test statistic works well.

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17

Nusrat, Sabrina, Muhammad Jawaherul Alam, Carlos Scheidegger, and Stephen Kobourov. "Cartogram Visualization for Bivariate Geo-Statistical Data." IEEE Transactions on Visualization and Computer Graphics 24, no. 10 (October 1, 2018): 2675–88. http://dx.doi.org/10.1109/tvcg.2017.2765330.

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18

Maxwell, Scott E., and Harold D. Delaney. "Bivariate median splits and spurious statistical significance." Psychological Bulletin 113, no. 1 (1993): 181–90. http://dx.doi.org/10.1037/0033-2909.113.1.181.

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19

Pourmousa, Reza, and Ahad Jamalizadeh. "On Bivariate Order Statistics from Elliptical Distributions." Communications in Statistics - Theory and Methods 43, no. 10-12 (April 23, 2014): 2183–98. http://dx.doi.org/10.1080/03610926.2013.861488.

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20

Su, C. C., L. Cormack, and A. Bovik. "Bivariate Statistics and Correlations in Natural Images." Journal of Vision 14, no. 10 (August 22, 2014): 651. http://dx.doi.org/10.1167/14.10.651.

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21

Jaafari, Abolfazl, Davood Mafi-Gholami, Binh Thai Pham, and Dieu Tien Bui. "Wildfire Probability Mapping: Bivariate vs. Multivariate Statistics." Remote Sensing 11, no. 6 (March 13, 2019): 618. http://dx.doi.org/10.3390/rs11060618.

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Wildfires are one of the most common natural hazards worldwide. Here, we compared the capability of bivariate and multivariate models for the prediction of spatially explicit wildfire probability across a fire-prone landscape in the Zagros ecoregion, Iran. Dempster–Shafer-based evidential belief function (EBF) and the multivariate logistic regression (LR) were applied to a spatial dataset that represents 132 fire events from the period of 2007–2014 and twelve explanatory variables (altitude, aspect, slope degree, topographic wetness index (TWI), annual temperature, and rainfall, wind effect, land use, normalized difference vegetation index (NDVI), and distance to roads, rivers, and residential areas). While the EBF model successfully characterized each variable class by four probability mass functions in terms of wildfire probabilities, the LR model identified the variables that have a major impact on the probability of fire occurrence. Two distribution maps of wildfire probability were developed based upon the results of each model. In an ensemble modeling perspective, we combined the two probability maps. The results were verified and compared by the receiver operating characteristic (ROC) and the Wilcoxon Signed-Rank Test. The results showed that although an improved predictive accuracy (AUC = 0.864) can be achieved via an ensemble modeling of bivariate and multivariate statistics, the models fail to individually provide a satisfactory prediction of wildfire probability (EBFAUC = 0.701; LRAUC = 0.728). From these results, we recommend the employment of ensemble modeling approaches for different wildfire-prone landscapes.

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22

Genest, Christian, and Louis-Paul Rivest. "Statistical Inference Procedures for Bivariate Archimedean Copulas." Journal of the American Statistical Association 88, no. 423 (September 1993): 1034–43. http://dx.doi.org/10.1080/01621459.1993.10476372.

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23

Ratnaparkhi, Makarand V., Subrahmaniam Kocherlakota, and Kathleen Kocherlakota. "Bivariate Discrete Distribution." Journal of the American Statistical Association 89, no. 425 (March 1994): 363. http://dx.doi.org/10.2307/2291248.

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24

Walhin, J. F. "Bivariate Hofmann distributions." Journal of Applied Statistics 30, no. 9 (November 2003): 1033–46. http://dx.doi.org/10.1080/0266476032000076155.

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25

Zhao, Jin, Humaira Faqiri, Zubair Ahmad, Walid Emam, M. Yusuf, and A. M. Sharawy. "The Lomax-Claim Model: Bivariate Extension and Applications to Financial Data." Complexity 2021 (May 4, 2021): 1–17. http://dx.doi.org/10.1155/2021/9993611.

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Анотація:

The uses of statistical distributions for modeling real phenomena of nature have received considerable attention in the literature. The recent studies have pointed out the potential of statistical distributions in modeling data in applied sciences, particularly in financial sciences. Among them, the two-parameter Lomax distribution is one of the prominent models that can be used quite effectively for modeling data in management sciences, banking, finance, and actuarial sciences, among others. In the present article, we introduce a new three-parameter extension of the Lomax distribution via using a class of claim distributions. The new model may be called the Lomax-Claim distribution. The parameters of the Lomax-Claim model are estimated using the maximum likelihood estimation method. The behaviors of the maximum likelihood estimators are examined by conducting a brief Monte Carlo study. The potentiality and applicability of the Lomax claim model are illustrated by analyzing a dataset taken from financial sciences representing the vehicle insurance loss data. For this dataset, the proposed model is compared with the Lomax, power Lomax, transmuted Lomax, and exponentiated Lomax distributions. To show the best fit of the competing distributions, we consider certain analytical tools such as the Anderson–Darling test statistic, Cramer–Von Mises test statistic, and Kolmogorov–Smirnov test statistic. Based on these analytical measures, we observed that the new model outperforms the competitive models. Furthermore, a bivariate extension of the proposed model called the Farlie–Gumble–Morgenstern bivariate Lomax-Claim distribution is also introduced, and different shapes for the density function are plotted. An application of the bivariate model to GDP and export of goods and services is provided.

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26

Papageorgiou, H. "Bivariate short distributions." Communications in Statistics - Theory and Methods 15, no. 3 (January 1986): 893–905. http://dx.doi.org/10.1080/03610928608829158.

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27

Zheng, Yanting, Jingping Yang, and Jianhua Z. Huang. "Approximation of bivariate copulas by patched bivariate Fréchet copulas." Insurance: Mathematics and Economics 48, no. 2 (March 2011): 246–56. http://dx.doi.org/10.1016/j.insmatheco.2010.11.002.

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28

Chiavone, Flávia Barreto Tavares, Claúdia Cristiane Filgueira Martins Rodrigues, Larissa De Lima Ferreira, Pétala Tuani Candido de Oliveira Salvador, Manaces Dos Santos Bezerril, and Viviane Euzebia Pereira Santos. "Clima Organizacional em uma Unidade de Terapia Intensiva: percepções da equipe de enfermagem." Enfermería Global 20, no. 2 (April 1, 2021): 390–425. http://dx.doi.org/10.6018/eglobal.427861.

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Objetivo: Medir el clima organizacional del equipo de enfermería en la unidad de cuidados intensivos. Método: Este es un estudio transversal, con enfoque cuantitativo, desarrollado en una unidad de cuidados intensivos de un hospital universitario en el noreste de Brasil. La recolección de datos se realizó en 2016, con la participación de 30 profesionales de enfermería. Se realizó el análisis de datos a partir de estadística descriptiva y análisis de datos bivariados. Resultados: Se encontró que los profesionales de enfermería perciben un clima organizacional bajo en el sector en que trabajan y el desarrollo profesional y los beneficios fueron el factor considerado más bajo entre los trabajadores. El análisis bivariado infiere significativamente que los profesionales que tienen hijos tienen una baja percepción del clima organizacional. Conclusión: La percepción del clima organizacional del equipo de enfermería investigado es baja. Objective: To measure the organizational climate of the nursing team in the intensive care unit. Method: This is a cross-sectional study, with a quantitative approach, developed in the intensive care unit of a university hospital in the Northeast of Brazil. Data collection was carried out in 2016, with the participation of 30 nursing professionals. Data analysis was carried out using descriptive statistics and a bivariate analysis of data. Results: It was found that nursing professionals perceive a low organizational climate score in the sector they work. The professional Development and the benefits were considered the lowest factor by the workers. The bivariate analysis significantly infers that the professionals who have children have a low perception of the organizational climate. Conclusion: The nursing team investigated is perceives the score of the organizational climate to be low. Objetivo: Mensurar o clima organizacional da equipe enfermagem na unidade de terapia intensiva. Método: trata-se de um estudo transversal, de abordagem quantitativa, desenvolvida em uma unidade de terapia intensiva em um hospital universitário no nordeste do Brasil. A coleta de dados foi realizada em 2016, com a participação de 30 profissionais de enfermagem. A análise dos dados se deu por estatística descritiva e análise bivariada dos dados. Resultados: Verificou-se que os profissionais de enfermagem percebem um baixo clima organizacional no setor que atuam e o Desenvolvimento profissional e benefícios foi o fator considerado mais baixo entre os trabalhadores. A análise bivariada infere de maneira significativa que os profissionais que possuem filhos têm uma baixa percepção do clima organizacional. Conclusão: A percepção do clima organizacional da equipe de enfermagem investigada é baixa.

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29

Han, Ruijian, Kani Chen, and Chunxi Tan. "Bivariate gamma model." Journal of Multivariate Analysis 180 (November 2020): 104666. http://dx.doi.org/10.1016/j.jmva.2020.104666.

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30

Walhin, Jean François. "Bivariate ZIP Models." Biometrical Journal 43, no. 2 (May 2001): 147–60. http://dx.doi.org/10.1002/1521-4036(200105)43:2<147::aid-bimj147>3.0.co;2-5.

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31

EREM, Ayşegül. "An exceedance model based on bivariate order statistics." Communications Faculty Of Science University of Ankara Series A1Mathematics and Statistics 70, no. 2 (December 31, 2021): 785–95. http://dx.doi.org/10.31801/cfsuasmas.816462.

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32

Ombao, Hernando C., Jonathan A. Raz, Rainer von Sachs, and Beth A. Malow. "Automatic Statistical Analysis of Bivariate Nonstationary Time Series." Journal of the American Statistical Association 96, no. 454 (June 2001): 543–60. http://dx.doi.org/10.1198/016214501753168244.

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33

Mendes, Jos Ricardo, and Michel Daoud Yacoub. "A General Bivariate Ricean Model and Its Statistics." IEEE Transactions on Vehicular Technology 56, no. 2 (March 2007): 404–15. http://dx.doi.org/10.1109/tvt.2007.891464.

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34

Filzmoser, Peter, Karel Hron, and Clemens Reimann. "The bivariate statistical analysis of environmental (compositional) data." Science of The Total Environment 408, no. 19 (September 1, 2010): 4230–38. http://dx.doi.org/10.1016/j.scitotenv.2010.05.011.

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35

Lechner, Richard, Markus Passenbrunner, and Joscha Prochno. "Estimating Averages of Order Statistics of Bivariate Functions." Journal of Theoretical Probability 30, no. 4 (July 9, 2016): 1445–70. http://dx.doi.org/10.1007/s10959-016-0702-8.

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36

Frei, Oleksandr, Olav Smeland, Dominic Holland, Alexey Shadrin, Wesley Thompson, Ole Andreassen, and Anders Dale. "BIVARIATE GAUSSIAN MIXTURE MODEL FOR GWAS SUMMARY STATISTICS." European Neuropsychopharmacology 29 (2019): S898—S899. http://dx.doi.org/10.1016/j.euroneuro.2017.08.211.

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37

Dehling, Herold, and Murad S. Taqqu. "Bivariate symmetric statistics of long-range dependent observations." Journal of Statistical Planning and Inference 28, no. 2 (June 1991): 153–65. http://dx.doi.org/10.1016/0378-3758(91)90023-8.

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38

Ye, Cinan. "Statistical inference procedure for a bivariate exponential distribution." Acta Mathematicae Applicatae Sinica 10, no. 1 (January 1994): 75–89. http://dx.doi.org/10.1007/bf02006261.

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39

Khan, et al., M. J. S. "Order Statistics from Bivariate Log-Exponentiated Kumarswamy Distribution." International Journal of Computational and Theoretical Statistics 4, no. 1 (May 1, 2017): 1–12. http://dx.doi.org/10.12785/ijcts/040101.

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40

Erem, Aysegul. "Bivariate two sample test based on exceedance statistics." Communications in Statistics - Simulation and Computation 49, no. 9 (January 24, 2019): 2389–401. http://dx.doi.org/10.1080/03610918.2018.1520868.

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41

Bantan, Rashad A. R., Shakaiba Shafiq, M. H. Tahir, Ahmed Elhassanein, Farrukh Jamal, Waleed Almutiry, and Mohammed Elgarhy. "Statistical Analysis of COVID-19 Data: Using A New Univariate and Bivariate Statistical Model." Journal of Function Spaces 2022 (June 23, 2022): 1–26. http://dx.doi.org/10.1155/2022/2851352.

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In this paper, a new distribution named as unit-power Weibull distribution (UPWD) defined on interval (0,1) is introduced using an appropriate transformation to the positive random variable of the Weibull distribution. This work offers quantile function, linear representation of the density, ordinary and incomplete moments, moment-generating function, probability-weighted moments, L -moments, TL-moments, Rényi entropy, and MLE estimation. Additionally, several actuarial measures are computed. The real data applications are carried out to underline the practical usefulness of the model. In addition, a bivariate extension for the univariate power Weibull distribution named as bivariate unit-power Weibull distribution (BIUPWD) is also configured. To elucidate the bivariate extension, simulation analysis and application using COVID-19-associated fatality rate data from Italy and Belgium to conform a BIUPW distribution with visual depictions are also presented.

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42

Chen, Zhenmin. "Pyramidal Distribution: An Alternative Distribution for Bivariate Uniformity Test Power Comparison." International Journal of Reliability, Quality and Safety Engineering 26, no. 02 (March 25, 2019): 1950007. http://dx.doi.org/10.1142/s0218539319500074.

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The purpose of the multi-dimensional uniformity test is to check whether the underlying probability distribution, from which a random sample is drawn, differs from the multi-dimensional uniform distribution. The multi-dimensional uniformity test has applications in various fields such as biology, astronomy and computer science. Various statistical tests have been proposed for the multivariate uniformity. As a special case, the bivariate statistic test is discussed in this paper. To evaluate the performance of the uniformity tests, power comparison is the technique for selecting appropriate statistical test. The Monte Carlo simulations usually used to compare the power of the tests. Berrendero, Cuevas and Vazquez-Grande proposed a distance-to-boundary test, which was one of the latest published statistical tests for multi-dimensional uniformity [J. R. Berrendero, A. Cuevas and F. Vazquez-Grande, Testing multivariate uniformity: The distance-to-boundary method, Canad. J. Stat. 34 (2006) 693–707]. Chen and Hu proposed another test for multivariate uniformity [Z. Chen and T. Hu, Statistical test for bivariate uniformity, Adv. Stat. 2014 (2014) 740831]. Power comparison was conducted to compare these tests. In order to get more convincing power comparison results, more alternative distributions should be used when power study is conducted. This paper proposes a new bivariate distribution, named the pyramidal distribution, with support set [Formula: see text]. This distribution is quite flexible so that it can be used to produce different shapes of bivariate distributions. Because of that, the proposed distribution can be used as an alternative distribution in power comparison for bivariate uniformity test.

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43

Li, Johnson Ching-Hong, and Rory M. Waisman. "Probability of bivariate superiority: A non-parametric common-language statistic for detecting bivariate relationships." Behavior Research Methods 51, no. 1 (August 10, 2018): 258–79. http://dx.doi.org/10.3758/s13428-018-1089-5.

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44

Gaidai, Oleg, Yu Cao, Yihan Xing, and Junlei Wang. "Piezoelectric Energy Harvester Response Statistics." Micromachines 14, no. 2 (January 20, 2023): 271. http://dx.doi.org/10.3390/mi14020271.

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Safety and reliability are essential engineering concerns for energy-harvesting installations. In the case of the piezoelectric galloping energy harvester, there is a risk that excessive wake galloping may lead to instability, overload, and thus damage. With this in mind, this paper studies bivariate statistics of the extreme, experimental galloping energy harvester dynamic response under realistic environmental conditions. The bivariate statistics were extracted from experimental wind tunnel results, specifically for the voltage-force data set. Authors advocate a novel general-purpose reliability approach that may be applied to a wide range of dynamic systems, including micro-machines. Both experimental and numerically simulated dynamic responses can be used as input for the suggested structural reliability analysis. The statistical analysis proposed in this study may be used at the design stage, supplying proper characteristic values and safeguarding the dynamic system from overload, thus extending the machine’s lifetime. This work introduces a novel bivariate technique for reliability analysis instead of the more general univariate design approaches.

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45

Nadarajah, Saralees, and Samuel Kotz. "Some bivariate beta distributions." Statistics 39, no. 5 (October 2005): 457–66. http://dx.doi.org/10.1080/02331880500286902.

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46

Ristić, Miroslav M. "Stationary bivariate minification processes." Statistics & Probability Letters 76, no. 5 (March 2006): 439–45. http://dx.doi.org/10.1016/j.spl.2005.08.011.

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47

Walker, Stephen, and Pietro Muliere. "A bivariate Dirichlet process." Statistics & Probability Letters 64, no. 1 (August 2003): 1–7. http://dx.doi.org/10.1016/s0167-7152(03)00124-x.

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48

Balakrishnan, N., A. Stepanov, and V. B. Nevzorov. "North-east bivariate records." Metrika 83, no. 8 (February 3, 2020): 961–76. http://dx.doi.org/10.1007/s00184-020-00766-2.

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49

Modarres, Reza. "Tests of Bivariate Exchangeability." International Statistical Review 76, no. 2 (August 2008): 203–13. http://dx.doi.org/10.1111/j.1751-5823.2008.00046.x.

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50

Maydeu-Olivares, Alberto, Carlos García-Forero, David Gallardo-Pujol, and Jordi Renom. "Testing Categorized Bivariate Normality With Two-Stage Polychoric Correlation Estimates." Methodology 5, no. 4 (January 2009): 131–36. http://dx.doi.org/10.1027/1614-2241.5.4.131.

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Structural equation modeling (SEM) with ordinal indicators rely on an assumption of categorized normality. This assumption may be tested for pairs of variables using the likelihood ratio G2 or Pearson’s X2 statistics. For increased computational efficiency, SEM programs usually estimate polychoric correlations in two stages. However, two-stage polychoric estimates are not asymptotically efficient and G2 and X2 need not be asymptotically chi-square when the estimator is not efficient. Recently, Maydeu-Olivares and Joe (2005) have introduced a new statistic, Mn , that is asymptotically chi-square even for estimators that are not efficient. We investigate the behavior of G2, X2, and Mn when testing underlying bivariate normality with polychoric correlations estimated in two stages.

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