Abstract
We introduce a new four-parameter model called the Gumbel-Lomax distribution arising from the GumbelX 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 incomplete 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 statistics. 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.
Highlights
Many lifetime distributions have been constructed with a view for applications in several areas, in particular, survival analysis, reliability engineering, demography, actuarial study, hydrology and others
The model parameters are estimated by maximum likelihood and three goodness-of-fit statistics are used to compare this distribution with three other models, namely: the gamma-Lomax (GaLx) (Cordeiro et al, 2015), exponentiated Lomax (ELx) (Abdul-Moniem and Abdel-Hameed, 2012) and beta-Lomax (BLx) (Lemonte and Cordeiro, 2013)
The interest in developing more flexible statistical distributions remains strong in statistical theory and applications
Summary
Many lifetime distributions have been constructed with a view for applications in several areas, in particular, survival analysis, reliability engineering, demography, actuarial study, hydrology and others. A < b < ∞ and let F(x) be the cumulative distribution function (cdf) of a random variable X such that the link function W (·) : [0, 1] −→ [a, b] satisfies two conditions: (i) W (·) is differentiable and monotonically non-decreasing, and (ii) W (x) → a as x → −∞ and W (x) → b as x → ∞. Following Alzaatreh et al (2013), Tahir et al (2015a) defined and studied the Logistic-X family of distributions.
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