Abstract
This paper introduces the beta linear failure rate geometric (BLFRG) distribution, which contains a number of distributions including the exponentiated linear failure rate geometric, linear failure rate geometric, linear failure rate, exponential geometric, Rayleigh geometric, Rayleigh and exponential distributions as special cases. The model further generalizes the linear failure rate distribution. A comprehensive investigation of the model properties including moments, conditional moments, deviations, Lorenz and Bonferroni curves and entropy are presented. Estimates of model parameters are given. Real data examples are presented to illustrate the usefulness and applicability of the distribution.
Highlights
Let G(x; φ) be the cumulative distribution function of an absolutely continuous random variable X, where φ ∈ Ω is the parameter vector
When a = b = 1, the beta linear failure rate geometric (BLFRG) distribution reduces to the linear failure rate geometric (LFRG) distribution
We present the quantile function of the BLFRG distribution
Summary
Let G(x; φ) be the cumulative distribution function (cdf) of an absolutely continuous random variable X, where φ ∈ Ω is the parameter vector. Several well-known distributions that belong to the resilience parameter family include the exponentiated Weibull (EW) distribution (see Mudholkar et al (1995), generalized (or exponentiated) exponential distribution proposed by Gupta and Kundu (1999), and exponentiated type distributions introduced by Nadarajah and. The probability density function (pdf) and hazard (failure) rate functions of a BG distribution corresponding to the cdf in equation (1) are given by f(x; g(x;φ) B(a,b). Oluyede et al (2015) introduced and studied the log generalized Lindley-Weibull distribution and applied the model to lifetime data. Bidram et al (2013) introduced a new distribution that includes the Weibull-geometric distribution of Barreto-Souza et al (2010).
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