The Gumbel-Lomax Distribution: Properties and Applications

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.

Keywords

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