A generalized normal distribution. (English) Zbl 1121.62447

Summary: Undoubtedly, the normal distribution is the most popular distribution in statistics. In this paper, we introduce a natural generalization of the normal distribution and provide a comprehensive treatment of its mathematical properties. We derive expressions for the nth moment, the nth central moment, variance, skewness, kurtosis, mean deviation about the mean, mean deviation about the median, Rényi entropy, Shannon entropy, and the asymptotic distribution of the extreme order statistics. We also discuss estimation by the methods of moments and maximum likelihood and provide an expression for the Fisher information matrix.


62-XX Statistics
Full Text: DOI


[1] Gradshteyn I. S., Table of Integrals, Series, and Products, 6. ed. (2000) · Zbl 0981.65001
[2] Leadbetter M. R., Extremes and Related Properties of Random Sequences and Processes (1987)
[3] Prudnikov A. P., Integrals and Series 1 (1990)
[4] Rényi, A. On measures of entropy and information. Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability. Vol. I, pp.547–561. Berkeley: University of California Press.
[5] DOI: 10.1016/S0378-3758(00)00169-5 · Zbl 0997.62003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.