4028

Hamed Mahmoodian

مجله پژوهشهاي آماري ايران

Statistical Research and Training Center پژوهشكده آمار

2020

17

1

95-111

Geometric distribution , power normal distribution , EM algorithm

In this paper, we introduce a new skewed distribution of which normal and power normal distributions are two special cases. This distribution is obtained by taking geometric maximum of independent identically distributed power normal random variables. We call this distribution as the power normal–geometric distribution. Some mathematical properties of the new distribution are presented. Maximum likelihood estimates of parameters are obtained via an EM algorithm. Simulation experiments have been presented to eva‎luate the performance of the maximum likelihood. We analyze two data sets for illustrative purposes. Finally, we derive a bivariate version of the proposed distribution.