A Three-Parameter Weighted Lindley Distribution and its Applications to Model Survival Time

Abstract

In this paper a three-parameter weighted Lindley distribution, including Lindley distribution introduced by Lindley (1958), a two-parameter gamma distribution, a two-parameter weighted Lindley distribution introduced by Ghitany et al. (2011) and exponential distribution as special cases, has been suggested for modelling lifetime data from engineering and biomedical sciences. The structural properties of the distribution including moments, coefficient of variation, skewness, kurtosis and index of dispersion have been derived and discussed. The reliability properties, including hazard rate function and mean residual life function, have been discussed. The estimation of its parameters has been discussed using the maximum likelihood method and the applications of the distribution have been explained through some survival time data of a group of patients suffering from head and neck cancer, and the fit has been compared with a one-parameter Lindley distribution and a two-parameter weighted Lindley distribution.

On Poisson-Weighted Lindley Distribution and Its Applications

“…Shanker et al [9] discussed various moments based properties including coefficient of variation, coefficient of skewness, coefficient of kurtosis and index of dispersion of WLD and its applications to model lifetime data from biomedical sciences and engineering. Shanker et al [10] have proposed a three-parameter weighted Lindley distribution (TPWLD) which includes one parameter exponential and Lindley distributions, two parameter gamma and weighted Lindley distributions as particular cases and discussed its various structural properties, estimation of parameters and applications for modeling lifetime data from engineering and biomedical sciences. The main purpose of this paper is to discuss the nature and behavior of the coefficient of variation, skewness, kurtosis and index of dispersion of Poisson-Weighted Lindley distribution (P-WLD), a Poisson mixture of weighted Lindley distribution.…”

On Modeling of Lifetime Data Using One Parameter Akash, Lindley and Exponential Distributions

“…The Lindley distribution is a two-component mixture of an exponential distribution having scale parameter θ and a gamma distribution having shape parameter 2 and scale parameter θ with mixing proportions and and is given by Lindley 6 in the context of Bayesian Statistics as a counter example of fiducial Statistics. A detailed study about its various mathematical properties, estimation of parameter and application showing the superiority of Lindley distribution over exponential distribution for the waiting times before service of the bank customers has been done by Ghitany et al, 7 The Lindley distribution has been generalized, extended, mixed, modified and its detailed applications in reliability and other fields of knowledge by different researchers including Sankaran 8 Hussain, 9 Zakerzadeh & Dolati, 10 Nadarajah et al, 11 Deniz & Ojeda, 12 Mazucheli & Achcar, 13 Bakouch et al, 14 Shanker & Mishra, 15,16 Shanker et al, 17 Shanker & Amanuel, 18 Elbatal et al, 19 Ghitany et al, 20 Merovci, 21 Liyanage & Pararai, 22 Ashour & Eltehiwy, 23 Oluyede & Yang, 24 Singh et al, 25 Sharma et al, 26 Shanker et al, 27 Alkarni, 28 Pararai et al, 29 Abouammoh et al, 30 are some among others.…”

Generalized Weighted Rama Distribution: Properties and Application to Model Lifetime Data

“…Recently, several weighted distributions have been developed and applied to many real life phenomena. Notable among them are the new class of weighted exponential distribution due to Gupta and Kundu [8], weighted Weibull proposed by Dey et al [9], weighted exponential by Dey et al [10], weighted Lindley introduced by Ghitany et al [11], weighted Maxwell by Joshi and Modi [12], new weighted Lindley due to Asgharzadeh et al [13], weighted Akash by Shanker and Shukla [14], weighted Shanker due to Shanker and Shukla [15], three-parameter weighted Lindley proposed by Shanker et al [16], weighted exponentiated Mukherjee-Islam by Subramanian and Rather [17], two-parameter weighted Sujatha due to Shanker and Shukla [18], three-parameter weighted Pareto Type II by Para and Jan [19], two-parameter weighted Rama due to Eyob and Shanker [20], weighted quasi Akash developed by Eyob et al [21], weighted exponential-Gompertz by Abd and Ragab [22], weighted Aradhana due to Ganaie et al [23], weighted Sushila by Rather [24], weighted Akshaya due to Rather and Subramanian [25], Weighted Odoma by Manoj and Elangovan [26], weighted new quasi Lindley Ganaie et al [27], weighted three-parameter Akash by Ganaie and Rajagopalan [28], weighted two parametric Rama by Vijayakumar et al [29], weighted Suja by Alsmairan and Al-Omari [30] among others. The aim of this paper is to introduce a generalized weighted Rama (GWR) distribution having three parameters.…”