The Lindley Weibull Distribution: properties and applications

Abstract

We introduce a new three-parameter lifetime model called the Lindley Weibull distribution, which accommodates unimodal and bathtub, and a broad variety of monotone failure rates. We provide a comprehensive account of some of its mathematical properties including ordinary and incomplete moments, quantile and generating functions and order statistics. The new density function can be expressed as a linear combination of exponentiated Weibull densities. The maximum likelihood method is used to estimate the model parameters. We present simulation results to assess the performance of the maximum likelihood estimation. We prove empirically the importance and flexibility of the new distribution in modeling two data sets.

Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

“…The moment estimates (MEs) of α and λ, denoted byα M E andλ M E , of the APE distribution can be obtained by equating the first two sample moments with the first two theoretical moments obtained from (8).…”

The quasi xgamma-geometric distribution with application in medicine

“…respectively, where µ 1 (µ X ) and µ 1 (M) can be numerically computed from (10), and F(µ X ) can be numerically computed from (7).…”

The odd inverse Pareto-G class: properties and applications

“…The data contain 128 observations on the remission times (in months) of bladder cancer patients (Lee and Wang, [21]). We shall compare the fits of the OIPLi distribution with some competitive models namely: the Lindley Weibull (LiW) (Cordeiro et al, [10]), transmuted two-parameter Lindley (TTLi) (Kemaloglu and Yilmaz, [18]), Weibull Lindley (WLi) (Asgharzadeh et al, [7]), Quasi Lindley (QLi ) (Shanker and Mishra, [29]), complementary geometric transmuted Lindley (CGcTLi) (Afify et al, [3]), generalized Lindley (GLi) (Nadarajah et al, [26]), new weighted Lindley (NWLi) (Asgharzadeh et al, [6]), and Lindley distributions whose PDFs are given by…”