The Alpha power Gompertz distribution: characterization, properties, and applications
type: Item
instance of: scholarly article
title: The Alpha power Gompertz distribution: characterization, properties, and applications
zbMATH Open document ID: 1466.62249
author: J. T. Eghwerido
author: Lawrence Chukwudumebi Nzei
author: Friday Ikechukwu Agu
published in: Sankhyā. Series A
publication date: 2021-05-03T00:00:00Z
review text: The authors investigate properties of the random variable with parameters \(\alpha\),\(\beta\),\(\lambda>0\) and distribution function given by \[ F_{\alpha,\beta,\lambda}(x)=\frac{1}{\alpha-1}\left(\alpha^{1-\exp\left\{-\frac{\lambda}{\beta}\left[\exp\left\{\beta x\right\}-1\right]\right\}}-1\right)\,, \] for \(x>0\) in the case where \(\alpha\not=1\). In the case where \(\alpha=1\), the distribution function is given by \[ F_{1,\beta,\lambda}(x)=1-\exp\left\{-\frac{\lambda}{\beta}\left[\exp\left\{\beta x\right\}-1\right]\right\}\,, \] for \(x>0\). Properties of this distribution investigated in the present paper include quantiles, moments, entropy, hazard rate, order statistics, and maximum likelihood estimation of parameters. The authors also show how this distribution can be represented as a mixture of Gompertz distributions, and conclude with numerical examples to illustrate the application of this distribution to data.
reviewed by: Fraser Daly
Mathematics Subject Classification ID: 62E10
Mathematics Subject Classification ID: 62E15
zbMATH DE Number: 7342657
zbMATH Keywords: Alpha power distribution
zbMATH Keywords: Gompertz distribution
MaRDI profile type: Publication
full work available at URL: s13171-020-00198-0
OpenAlex ID: W3012948015
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DOI: 10.1007/S13171-020-00198-0
description: scientific article; zbMATH DE number 7342657