A generalized normal distribution

Saralees Nadarajah

Journal of Applied Statistics, 2005, vol. 32, issue 7, 685-694

Abstract: 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, Renyi 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.

Keywords: Estimation; entropy; generalized normal distribution; moments; normal distribution; order statistics (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (38)

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DOI: 10.1080/02664760500079464

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