A new generalized normal distribution: Properties and applications

Mohammad A. Aljarrah; Felix Famoye; Carl Lee

doi:10.1080/03610926.2018.1483509

A new generalized normal distribution: Properties and applications

Mohammad A. Aljarrah, Felix Famoye, Carl Lee

Statistics, Actuarial & Data Sciences

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	4474-4491
Number of pages	18
Journal	Communications in Statistics - Theory and Methods
Volume	48
Issue number	18
DOIs	https://doi.org/10.1080/03610926.2018.1483509
State	Published - Sep 17 2019

Keywords

Beta-family
entropy
hazard function
moments
symmetrical distribution

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10.1080/03610926.2018.1483509

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title = "A new generalized normal distribution: Properties and applications",

abstract = "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.",

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AU - Aljarrah, Mohammad A.

AU - Famoye, Felix

AU - Lee, Carl

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AB - 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.

KW - Beta-family

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KW - hazard function

KW - moments

KW - symmetrical distribution

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A new generalized normal distribution: Properties and applications

Abstract

Keywords

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