# The gamma-normal distribution: Properties and applications

Ayman Alzaatreh, Felix Famoye, Carl Lee

Research output: Contribution to journalArticle

38 Citations (Scopus)

### Abstract

In this paper, some properties of gamma-X family are discussed and a member of the family, the gamma-normal distribution, is studied in detail. The limiting behaviors, moments, mean deviations, dispersion, and Shannon entropy for the gamma-normal distribution are provided. Bounds for the non-central moments are obtained. The method of maximum likelihood estimation is proposed for estimating the parameters of the gamma-normal distribution. Two real data sets are used to illustrate the applications of the gamma-normal distribution.

Original language English 67-80 14 Computational Statistics and Data Analysis 69 https://doi.org/10.1016/j.csda.2013.07.035 Published - 2014 Yes

### Fingerprint

Gamma distribution
Normal distribution
Gaussian distribution
Moment
Mean deviation
Shannon Entropy
Maximum likelihood estimation
Limiting Behavior
Maximum Likelihood Estimation
Entropy
Family

### Keywords

• Estimation
• Hazard function
• Moments
• T-X distributions

### ASJC Scopus subject areas

• Computational Mathematics
• Computational Theory and Mathematics
• Statistics and Probability
• Applied Mathematics

### Cite this

The gamma-normal distribution : Properties and applications. / Alzaatreh, Ayman; Famoye, Felix; Lee, Carl.

In: Computational Statistics and Data Analysis, Vol. 69, 2014, p. 67-80.

Research output: Contribution to journalArticle

Alzaatreh, Ayman ; Famoye, Felix ; Lee, Carl. / The gamma-normal distribution : Properties and applications. In: Computational Statistics and Data Analysis. 2014 ; Vol. 69. pp. 67-80.
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