Normality for Non-normal Distributions
DOI:
https://doi.org/10.37134/jsml.vol8.2.7.2020Keywords:
normal, sample size, Poisson, Exponential, GammaAbstract
It has been usually assumed that a sample data is normally distributed when the sample size is at least 30. This is the general rule in using central limit theorem based on the sample size being greater or equal to 30. Many literary works also assumed normality when sample size is at least 30. This study aims to determine the least required sample size that satisfy normality assumption from three non-normal distributions, Poisson, Gamma and Exponential distributions. Computer simulations are carried out to study the least required sample size for the three distributions. Through the study, it is found that sample data from Poisson and Gamma distributions need sample size less than 30, while Exponential needs more than 30 to achieve normality.
Downloads
References
Anacleto, O. (2018, February). Introduction to probability distributions. South Bridge, Edinburgh, The United Kingdom.
Bian, H. (2016). Non-parametric Tests. Retrieved January 2, 2020, from
http://core.ecu.edu/ofe/statisticsresearch/Non-Parametric%20Tests.pdf
Chang, H. J., Huang, K. C., & Wu, C. H. (2006). Determination of Sample Size in Using Central Limit Theorem for Weibull Distribution. Information and Management Sciences, 17(3), 31-46.
Chang, H. J., Wu, C. H., Ho, J. F., & Chen, P. Y. (2008). On Sample Size in Using Central Limit Theorem for Gamma Distribution. Information and Management Sciences, 19(1), 153-174.
Das, K. R., & Imon, A. H. (2016). A Brief Review of Tests for Normality. American Journal of Theoretical and Applied Statistics, 5-12.
Epstein, B. (1958). The Exponential Distribution and Its Role in Life Testing. Michigan: Department of Mathematics, Wayne State University.
Kwak, S. G., & Kim, J. H. (2017). Central Limit Theorem: the cornerstone of modern statistics. Statistical Round, 144-156.
Kiche, J., Ngesa, O. & Orwa, G. (2019). On Generalized Gamma Distribution and Its Application to Survival Data. International Journal of Statistics and Probability, 8(5), 85-102.
Laha, A. K. (2006). A Note on Tests of Normality. Ahmedabad: Indian Institute of Management.
Miller, I., & Miller, M. (2014). John E. Freund's Mathematical Statistics with Applications. Pearson Education Limited.
NCSS.com. (n.d.). Normality Tests. Retrieved January 2, 2020, from
https://ncss-wpengine.netdna-ssl.com/wp-content/themes/ncss/pdf/Procedures/NCSS/Normality_Tests.pdf
Smith, Z. R., & Wells, C. S. (2006). Central Limit Theorem and Sample Size. New York: University of Massachusetts Amherst.
Stine, R. A. (2016). Explaining Normal Quantile-Quantile Plots through. The American Statistician, 145-147.
Tse, K.-K. (2014). Some Applications of the Poisson Process. Applied Mathematics, 3011-3017.
Yap, B. W., & Sim, C. H. (2011). Comparisons of various types of normality tests. Journal of Statistical Computation and Simulation, 2141-2155.
