The Gumbel-Lomax Distribution: Properties and Applications

DOI

10.2991/jsta.2016.15.1.6How to use a DOI?

Keywords

Characterization; Gumbel distribution; Gumbel-X family; Lomax distribution; Shannon entropy; T-X family.

Abstract

We introduce a new four-parameter model called the Gumbel-Lomax distribution arising from the Gumbel- X generator recently proposed by Al-Aqtash (2013). Its density function can be right-skewed and reversed-J shaped, and can have decreasing and upside-down bathtub shaped hazard rate. Various structural properties of the new distribution are obtained including explicit expressions for the quantile function, ordinary and incom- plete moments, Lorenz and Bonferroni curves, mean residual lifetime, mean waiting time, probability weighted moments, generating function and Shannon entropy. We also provide the density function for the order statis- tics. Some characterizations of the new distribution based on the conditional expectations of certain functions of the random variable are also proposed. The model parameters are estimated by the method of maximum likelihood and the observed information matrix is determined. The flexibility of the new model is illustrated by means of two real lifetime data sets.

Copyright

© 2017, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - M.H. Tahir
AU  - M. Adnan Hussain
AU  - Gauss M. Cordeiro
AU  - G.G. Hamedani
AU  - M. Mansoor
AU  - M. Zubair
PY  - 2016
DA  - 2016/03/01
TI  - The Gumbel-Lomax Distribution: Properties and Applications
JO  - Journal of Statistical Theory and Applications
SP  - 61
EP  - 79
VL  - 15
IS  - 1
SN  - 2214-1766
UR  - https://doi.org/10.2991/jsta.2016.15.1.6
DO  - 10.2991/jsta.2016.15.1.6
ID  - Tahir2016
ER  -