Abstract
A new four-parameter distribution called the beta Lindley-geometric distribution is proposed. The hazard rate function of the new model can be constant, decreasing, increasing, upside down bathtub or bathtub failure rate shapes. Various structural properties including of the new distribution are derived. The estimation of the model parameters is performed by maximum likelihood method. The usefulness of the new distribution is illustrated using a real data set.
Highlights
The Lindley distribution (Lindley, 1958) is important for studying stress-strength reliability modeling
The Lindley distribution specified by the probability density function (PDF)
We propose a new extension of the LGc distribution of Zakerzadeh and Mahmoudi (2012) by taking G(x; φ) in (3) to the cumulative distribution function (CDF) of the LGc distribution
Summary
The Lindley distribution (Lindley, 1958) is important for studying stress-strength reliability modeling. A new extension of the Lindley distribution, called extended Lindley distribution, which offers a more flexible model for lifetime data is introduced by Bakouch et al (2012). Zakerzadeh and Mahmoudi (2012) introduced the Lindley-geometric (LGc) distribution with CDF and PDF given by FLG (x, θ, p). A general class generated from the logit of a beta random variable is introduced by Eugene et al (2002) and it is called the beta-G (B-G) family with the CDF. The two classes given in (iv) and (v) are called, respectively, the frailty parameter and resilience parameter families with underlying distribution G(x; φ) (Marshall and Olkin, 2007). The new model is referred to as the beta Lindley geometric (BLGc) distribution.
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