Lindley–Exponential distribution: properties and applications

Abstract

In this paper, we introduce a new distribution generated by Lindley random variable which offers a more flexible model for modelling lifetime data. Various statistical properties like distribution function, survival function, moments, entropy, and limiting distribution of extreme order statistics are established . Inference for a random sample from the proposed distribution is investigated and maximum likelihood estimation method is used for estimating parameters of this distribution. The applicability of the proposed distribution is shown through real data sets.

Minimum Variance Unbiased Estimation of Reliability Function for a Class of Generalizations of Lindley Distribution

“…However, the major drawback of Lindley distribution is its increasing failure rate property and this opened the scope of generalizing the distribution. Naturally, the generalizations are not unique and cover different aspects, and the list includes generalized Lindley distribution of Zakerzadeh and Dolati [3] , extended Lindley distribution of Bakouch et al [4] , power Lindley distribution of Ghitanty et al [5] , two-parameter Lindley distribution of Shanker and Sharma [6] , Lindley-Exponential distribution of Bhati et al [7] , another generalized Lindley distribution of Abouammoh et al [8] , inverse Lindley distribution and its extension of Sharma and Khandelwal [9] , the odd Lindley Burr XII distribution of Abouelmagd et al [10] and the exponential Lindley odd log-logistic G family of Korkmaz et al, [11] among others. However, none of these generalizations provides the most desirable bathtub shape failure rate.…”

A new model for describing remission times: the generalized beta-generated Lindley distribution

“…The GBGL model provides the best fit to these data among the current models. Thus, our proposal can be a competitive distribution compared with other extended Lindley models: L, L exponential (Bhati and Malik 2015) and GL. In this paper, we propose a new four-parameter distribution called the generalized beta-generated Lindley (GBGL) model.…”

“…• The Lindley-exponential (LE) model (Bhati and Malik 2015), whose pdf and cdf are, respectively, given by…”

Size Biased Lindley Distribution and Its Properties a Special Case of Weighted Distribution

“…The Lindley distribution introduced with two parameters by Shanker et al (2013) [1] by taking into account the survival and waiting time data. In Lindley exponential distribution Bhatti and Malik (2014) [2] studied its mathematical properties and checked its flexibility by using real data set.…”

“…Shanker et al (2013) [15] compared one parameter Lindley distribution with two parameter Lindley distribution. While Wang (2013) [16] introduced a life time distribution with three parameters, although Bhati and Malik (2014) [17] worked at Lindley random variable and bring in to being a new family of distribution for remission times uncensored data of 128 cancer bladder patients. Mervoci and Sharma (2014) [18] …”