A new generalized normal distribution: Properties and applications

The most commonly studied generalized normal distribution is the well-known skew-normal by Azzalini. In this paper, a new generalized normal distribution is defined and studied. The distribution is unimodal and it can be skewed right or left. The relationships between the parameters and the mean, va...

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Bibliographic Details
Published inCommunications in statistics. Theory and methods Vol. 48; no. 18; pp. 4474 - 4491
Main Authors Aljarrah, Mohammad A., Famoye, Felix, Lee, Carl
Format Journal Article
LanguageEnglish
Published Philadelphia Taylor & Francis 17.09.2019
Taylor & Francis Ltd
Subjects
Beta-family
entropy
hazard function
Kurtosis
Maximum likelihood estimates
moments
Normal distribution
Parameter estimation
Skewed distributions
Skewness
symmetrical distribution
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Summary:The most commonly studied generalized normal distribution is the well-known skew-normal by Azzalini. In this paper, a new generalized normal distribution is defined and studied. The distribution is unimodal and it can be skewed right or left. The relationships between the parameters and the mean, variance, skewness, and kurtosis are discussed. It is observed that the new distribution has a much wider range of skewness and kurtosis than the skew-normal distribution. The method of maximum likelihood is proposed to estimate the distribution parameters. Two real data sets are applied to illustrate the flexibility of the distribution.
ISSN:0361-0926
1532-415X
DOI:10.1080/03610926.2018.1483509