The Shifted Exponential Distribution is widely used in engineering and industrial applications. Goodness-of-fit procedures are revisited. Shapiro-Wilk test, Shapiro-Francia test, Likelihood-ratio Anderson-Darling test, and Likelihood-ratio Kolmogorov-Smirnov test are implemented in shifted exponential distribution. A comparative study with usual Anderson-Darling, Chi-square, Cramer-von-mises, and Kolmogorov-Smirnov tests in testing for shifted exponential distribution is performed using simulation. The Likelihood-ratio Anderson-Darling test is found to be of most powerful irrespective of variant alternatives considered.
References
[1]
Johnson, N.L. and Kotz, S. (1970) Continuous Univariate Distributions-1. Houghton Mifflin Company.
[2]
Johnson, N.L., Kotz, S. and Balakrishnan, N. (1994) Continuous Univariate Distri-butions-1. 2nd Edition, John Wiley & Sons, Inc.
[3]
Balakrishnan, N. and Basu, A.P. (1995) The Exponential Distribution: Theory, Methods and Applications. Gordon and Breach Publishers.
[4]
Balakrishnan, N. and Sandhu, R.A. (1996) Best Linear Unbiased and Maximum Likelihood Estimation for Exponential Distributions under General Progressive Type-II Censored Samples. Sankhya: TheIndianJournalofStatistics, SeriesB, PartI, 58, 1-9.
[5]
Rahman, M. and Pearson, L.M. (2001) Estimation in Two-Parameter Exponential Distributions. JournalofStatisticalComputationandSimulation, 70, 371-386. https://doi.org/10.1080/00949650108812128
[6]
Rahman, M. and Wu, H. (2017) Tests for Exponentiality: A Comparative Study. AmericanJournalofAppliedMathematicsandStatistics, 5, 125-135. https://doi.org/10.12691/ajams-5-4-3
[7]
Anderson, T.W. and Darling, D.A. (1954) A Test of Goodness of Fit. JournaloftheAmericanStatisticalAssociation, 49, 765-769. https://doi.org/10.1080/01621459.1954.10501232
[8]
Zhang, J. and Wu, Y. (2005) Likelihood-Ratio Tests for Normality. ComputationalStatistics&DataAnalysis, 49, 709-721. https://doi.org/10.1016/j.csda.2004.05.034
[9]
Kolmogorov, A. (1933) Sulla determinazione empirica di una legge di distribuzione. Giornale dell’Istituto Italiano degliAttuari, 4, 83-91.
[10]
Smirnov, N. (1948) Table for Estimating the Goodness of Fit of Empirical Distributions. TheAnnalsofMathematicalStatistics, 19, 279-281. https://doi.org/10.1214/aoms/1177730256
[11]
Shapiro, S.S. and Wilk, M.B. (1965) An Analysis of Variance Test for Normality (Complete Samples) Biometrika, 52, 591-611. https://doi.org/10.1093/biomet/52.3-4.591
[12]
Shapiro, S.S. and Francia, R.S. (1972) An Approximate Analysis of Variance Test for Normality. JournaloftheAmericanStatisticalAssociation, 67, 215-216. https://doi.org/10.1080/01621459.1972.10481232
[13]
Bain, L.J. and Engelhardt, M. (1992) Introduction to Probability and Mathematical Statistics. PWS-KENT Publishing Company.