The Beta Distribution is widely used in engineering and industrial applications. Goodness-of-fit procedures are revisited. Shapiro-Francia statistic is implemented in Beta distribution. A comparative study between the Anderson-Darling, Kolmogorov-Smirnov, Shapiro-Francia, and Chi-square goodness-of-fit test in testing for Beta distribution is performed using simulation.
References
[1]
Evans, M., Hastings, N., Peacock, B. et al. (2000) Statistical Distributions. 4th Edition, John Wiley & Sons Ltd.
[2]
Rahman, M. and Amin, M.I. (2024). A Note on Parameter Estimation in Beta Distribution. Far East Journal of Theoretical Statistics, 68, 255-262. https://doi.org/10.17654/0972086324015
[3]
Anderson, T. W. and Darling, D. A. (1954). A Test of Goodness-of-Fit. Journal of the American Statistical Association, 49, 765-769. https://doi.org/10.1080/01621459.1954.10501232
[4]
Kolmogorov, A., Kolmogorov, A.N. et al. (1933) Sulla determinazione empirica di una legge di distribuzione. Istituto Italiano degliAttuari. Giornale, 4, 83-91.
[5]
Smirnov, N. (1948) Table for Estimating the Goodness of Fit of Empirical Distributions. Annals of Mathematical Statistics, 19, 279-281. https://doi.org/10.1214/aoms/1177730256
[6]
Shapiro, S.S. and Francia, R.S. (1972) An Approximate Analysis of Variance Test for Normality. Journal of the American Statistical Association, 67, 215-216. https://doi.org/10.1080/01621459.1972.10481232
[7]
Rahman, M. and Pearson, L.M. (2000) Shapiro-Francia W`Statistic Using Exclusive Monte Carlo Simulation. Journal of the Korean Data & Information Science Society, 11, 139-155.
[8]
Raschke, M. (2011) Empirical Behavior of Tests for the Beta Distribution and Their Application in Environmental Research. Stochastic Environmental Research and Risk Assessment, 25, 79-89. https://doi.org/10.1007/s00477-010-0410-3