Goodness of Fit Tests for the Poisson Distribution with Unknown Parameter Using the New Critical Value Tables
Abstract
This study aims to establish the critical values tables for Kolmogorov-Smirnov, Cramer-von Mises and Anderson-Darling tests for the Poisson distribution with unknown parameter. Additionally, examined how well these tests performed when using the new critical value tables based on type I error rate and power of the test. The results showed that the Kolmogorov-Smirnov test could not control type I error as well as the Cramer-von Mises and Anderson-Darling tests. In almost every situation, the Cramer-von Mises test provided the most powerful test. Furthermore, as the sample size increase, the power of each test increases. Keywords : Poisson distribution ; Goodness of fit test ; Critical values ; Power of the test ; Type I errorReferences
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distributions. The Canadian Journal of Statistics, 22(1), 125-137.
Conover, W.J. (1972). A Kolmogorov Goodness-of-Fit Test for Discontinuous Distributions. Journal of the
American Statistical Association, 67(339), 591-596.
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for Discrete Distributions. Biometrika, 65(1), 235-239.
Gibbons, J.D., & Chakraborti, S. (2003). Nonparametric Statistical Inference: Revised and Expanded.
(4th ed.). CRC Press. https://doi.org/10.4324/9780203911563
Horn, S.D. (1977). Goodness-of-Fit Tests for Discrete Data: A Review and an Application to a Health
Impairment Scale. Biometrics, 33(1), 237-247.
Lockhart, R.A., Spinelli, J.J., & Stephens, M.A. (2007). Cramer-von Mises Statistics for Discrete Distributions
with Unknow Parameters. The Canadian Journal of Statistics, 35(1), 125-133.
Pettitt, A.N., & Stephens, M.A. (1977). The Kolmogorov-Smirnov Goodness-of-Fit Statistic with Discrete and
Grouped Data. Technometrics, 19(2), 205-210.
Spinelli, J.J., Stephens, M.A. (1997). Cramer-von Mises Tests of Fit for the Poisson distribution. The Canadian
Journal of Statistics, 25(2), 257-268.
144-152. https://doi.org/10.1111/j.2044-8317.1978.tb00581.x
Choulakian, V., Lockhart, R.A., & Stephens, M.A. (1994). Cramer-von Mises Statistics for Discrete
distributions. The Canadian Journal of Statistics, 22(1), 125-137.
Conover, W.J. (1972). A Kolmogorov Goodness-of-Fit Test for Discontinuous Distributions. Journal of the
American Statistical Association, 67(339), 591-596.
Constance L. Wood and Michele M. Altavela. (1978). Large-Sample Results for Kolmogorov-Smirnov Statistics
for Discrete Distributions. Biometrika, 65(1), 235-239.
Gibbons, J.D., & Chakraborti, S. (2003). Nonparametric Statistical Inference: Revised and Expanded.
(4th ed.). CRC Press. https://doi.org/10.4324/9780203911563
Horn, S.D. (1977). Goodness-of-Fit Tests for Discrete Data: A Review and an Application to a Health
Impairment Scale. Biometrics, 33(1), 237-247.
Lockhart, R.A., Spinelli, J.J., & Stephens, M.A. (2007). Cramer-von Mises Statistics for Discrete Distributions
with Unknow Parameters. The Canadian Journal of Statistics, 35(1), 125-133.
Pettitt, A.N., & Stephens, M.A. (1977). The Kolmogorov-Smirnov Goodness-of-Fit Statistic with Discrete and
Grouped Data. Technometrics, 19(2), 205-210.
Spinelli, J.J., Stephens, M.A. (1997). Cramer-von Mises Tests of Fit for the Poisson distribution. The Canadian
Journal of Statistics, 25(2), 257-268.
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Published
2023-05-11
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Research Article
