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 language | English |
|---|---|
| Pages (from-to) | 68-79 |
| Number of pages | 12 |
| Journal | Statistical Theory and Related Fields |
| Volume | 2 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - Jan 2 2018 |
Funding
Manat Mustafa is grateful to the Nazarbayev University for providing the financial support through Faculty Development Competitive Research Grants [grant number N090118FD5342].
Keywords
- Exponentiated-exponential
- moments
- order statistic
- Shannon entropy
- T-X family
- Weibull-X family
ASJC Scopus subject areas
- Analysis
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Computational Theory and Mathematics
- Applied Mathematics