A generalisation of the exponential distribution and its applications on modelling skewed data

Manat Mustafa, Muhammad Zubair, Ayman Alzaatreh, M. H. Tahir, Muhammad Mansoor

Research output: Contribution to journalArticle

Abstract

In this paper, a generalisation of the exponential distribution, namely, Weibull exponentiated-exponential (WEE) distribution, is proposed. The shapes of the density function possess great flexibility. It can accommodate various hazard shapes such as reversed-J, increasing, decreasing, constant and upside-down bathtub. Various properties of the WEE distribution are studied including shape properties, quantile function, expressions for the moments and incomplete moments, probability weighted moments and Shannon entropy. We obtain the asymptotic distributions for the sample minimum and maximum. The model parameters are estimated by maximum likelihood. The usefulness of the new model is illustrated by means of two real lifetime data sets.
Original languageEnglish
Article number1
Pages (from-to)68-79
JournalStatistical Theory and Related Fields
Volume2
Issue number1
Publication statusPublished - May 16 2018

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Exponential distribution
Weibull Distribution
Probability Weighted Moments
Modeling
Moment
Lifetime Data
Quantile Function
Shannon Entropy
Density Function
Hazard
Asymptotic distribution
Maximum Likelihood
Flexibility
Model
Generalization

Cite this

A generalisation of the exponential distribution and its applications on modelling skewed data. / Mustafa, Manat; Zubair, Muhammad; Alzaatreh, Ayman; Tahir, M. H.; Mansoor, Muhammad.

In: Statistical Theory and Related Fields , Vol. 2, No. 1, 1, 16.05.2018, p. 68-79.

Research output: Contribution to journalArticle

Mustafa, Manat ; Zubair, Muhammad ; Alzaatreh, Ayman ; Tahir, M. H. ; Mansoor, Muhammad. / A generalisation of the exponential distribution and its applications on modelling skewed data. In: Statistical Theory and Related Fields . 2018 ; Vol. 2, No. 1. pp. 68-79.
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