Modified Goodness of Fit Tests for Rayleigh Distribution

Authors

  • Vanida Pongsakchat Department of Mathematic, Faculty of Science, Burapha University, Chonburi, Thailand
  • Pattaraporn Tonhaseng Department of Mathematic, Faculty of Science, Burapha University, Chonburi, Thailand

DOI:

https://doi.org/10.24203/ajas.v10i1.6901

Keywords:

Goodness-of-fit test, Rayleigh distribution, Monte Carlo simulation, Power of the test

Abstract

The modified goodness of fit tests for the Rayleigh distribution are studied. The critical values of modified Kolmogorov-Smirnov, Cramer-von-Mises and Anderson-Darling tests are obtained by Monte Carlo simulation for different sample sizes and significant levels. The type I error rate and power of these tests are studied and compared. The results show that all of the three tests have type I error rate close to the significant levels. Under several alternative distributions, it is founded that when the sample size is large, modified Anderson-Darling has the largest power in all cases. However, when the sample size is small, skewness of the distribution plays an important role. For the more skewed distribution, the modified Anderson-Darling test has more power than the others, while the modified Cramer-von-Mises has the largest power when the distribution is less skewed.

References

Afify, W. M., Ramzy, A., “Modified Goodness of Fit Tests for the Inverse Flexible Weibull Distribution”, Advances and Applications in Statistics, vol. 48 no. 4, pp.257-272, 2016. DOI: 10.17654/AS048040257

Aslam M., Tahir M., Hussain Z., Al-Zahrani B. “A 3-Component Mixture of Rayleigh Distributions: Properties and Estimation in Bayesian Framework”, PLoS ONE 10(5): e0126183, 2015. DOI: 10.1371/journal.pone.0126183

Badr, M. M., “Goodness-of-Fit Tests for the Compound Rayleigh Distribution with Application to Real Data”, Heliyon, vol. 5, e0225, 2019.

Jahanshahi, S. M. A., Habibirad, A., Fakoor, V., “Some New Goodness-of-fit Tests for Rayleigh Distribution”, Pakistan Journal of Statistics and Operation Research, vol. 16, no. 2, pp.305-315, 2020.

Johnson, N. L., Kotz, S., Balakrishnan, N., Continuous Univariate Distributions Volume 1, 2nd edition, John Wiley & Sons, New York, 1994.

Lilliefors, H. W., “On the Kolmogorov-Smirnov Test for Normality with Mean and Variance Unknown”, Journal of the American Statistical Association, vol. 62, no. 318, pp.399–402, 1967. DOI: 10.2307/2283970

Lilliefors, H. W., “On the Kolmogorov-Smirnov Test for the Exponential Distribution with Mean Unknown”, Journal of the American Statistical Association, vol. 64, no. 325, pp.387-389, 1969. DOI: 10.1080/01621459.1969.10500983

Lord Rayleigh F.R.S., “XII. On the resultant of a large number of vibrations of the same pitch and of arbitrary phase”, The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, vol.10 no. 60, pp.73-78, 1880. DOI: 10.1080/14786448008626893

Shawky, A.I., Bahoban, R. A., “Modified Godness-of-Fit Tests for Exponentiated Gamma Distribution with Unknown Shape Parameter”, InterStat, vol. 3, Jan, pp.1-17, 2009.

Woodruff, B. W., Viviano, P. J., Moore, A. H., Dunne, E.J., “Modified Goodness- of-Fit Tests for Gamma Distribution with Unknown Location and Scale Parameters”, IEEE Transactions on Reliability, vol. R-33, no. 3, 1984.

Yen, V. C., Moore, A. H. “Modified Goodness-of-fit Test for the Laplace Distribution”, Communications in Statistics - Simulation and Computation, vol. 17, no. 1, pp.275-281, 1988. DOI: 10.1080/03610918808812661

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Published

2022-03-04

How to Cite

Pongsakchat, V., & Tonhaseng, P. (2022). Modified Goodness of Fit Tests for Rayleigh Distribution. Asian Journal of Applied Sciences, 10(1). https://doi.org/10.24203/ajas.v10i1.6901

Issue

Vol. 10 No. 1 (2022): February 2022

Section

Articles

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Copyright (c) 2022 Vanida Pongsakchat, Pattaraporn Tonhaseng

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