A generalized normal distribution

被引：333

作者：

Nadarajah, S ^{[1
]}

机构：

[1] Univ Nebraska, Dept Stat, Lincoln, NE 68583 USA

来源：

JOURNAL OF APPLIED STATISTICS | 2005年 / 32卷 / 07期

关键词：

estimation; entropy; generalized normal distribution; moments; normal distribution; order statistics;

D O I：

10.1080/02664760500079464

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

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.

引用

页码：685 / 694

页数：10