The Lindley Family of Distributions: Properties and Applications

Abstract

In this paper, we propose a new class of distributions called the Lindley generator with one extra parameter to generate many continuous distributions. The new distribution contains several distributions as submodels, such as Lindley-Exponential, Lindley-Weibull, and LindleyLomax. Some mathematical properties of the new generator, including ordinary moments, quantile and generating functions, limiting behaviors, some entropy measures and order statistics, which hold for any baseline model, are presented. Then, we discuss the maximum likelihood method to estimate model parameters. The importance of the new generator is illustrated by means of three real data sets. Applications show that the new family of distributions can provide a better fit than several existing lifetime models.

The Exponential Lindley Odd Log-Logistic-G Family: Properties, Characterizations and Applications

“…A new family of distributions called the exponential Lindley odd log-logistic G family is introduced and studied. The new family generalizes the Lindley-G family [9], Lehmann Type II-G family [19] and odd Burr-G family [4] as well as it introduces new distribution families such as exponential Lindley-G family and Lindley odd log-logistic-G family. We provide some mathematical properties of the new family including ordinary, generating function and order statistics.…”

“…This data set has been analyzed by Cordeiro et al [14]. Using this data set, we fit the ELOLL-N, Lindley-normal (L-N) (Ç akmakyapan and Ozel, [9]), exponential-normal (E-N) or Lehmann type II exponentiated-normal (Alzaatreh et al, [5]; Cordeiro et al [15]), McDonaldnormal (McN) (Alexander et al [3]), normal-normal{exponential} (NNE) (Alzaatreh et al [6]), normal-Cauchy{log-logistic} (NCLL) (Alzaatreh, et al [7]), logistic-normal (LN) (Tahir et al [32]), generelized Kumaraswamy-normal (GKw-N) (Cordeiro et al [11]) and generalized odd log-logistic normal (GOLLN) (Cordeiro, et al [10]) distributions models. The results of this application are listed in Table 3.…”

“…As second data analysis, we analyze the data set studied by Abouammoh et al [1], which represent the lifetime in days of 40 patients suffering from leukemia from one of the Ministry of Health Hospitals in Saudi Arabia. By using this data set we compare the ELOLL-W distribution with logistic-Weibull (LW) (Tahir et al [32]), odd-Burr-Weibull (OBW) (Alizadeh et al [4]), Lindley-Weibull (L-W) (Ç akmakyapan and Ozel [9]) and exponential-Weibull (E-W) or ordinary Weibull distributions. The results of this application are listed in Table 4.…”

A Power Gompertz Distribution: Model, Properties and Application to Bladder Cancer Data

“…New families of distributions are produced day by day and are useful for adding parameters to all forms of probability distributions which makes the resulting distribution more flexible for modeling heavily skewed dataset. Some of these families of distributions include the beta generalized family (Beta-G) by Eugene et al [7], Transmuted family of distributions by Shaw and Buckley [8], Gamma-G (type 1) by Zografos and Balakrishnan [9], the Kumaraswamy-G by Cordeiro and de Castro [10], McDonald-G by Alexander et al [11], Gamma-G (type 2) by Ristic et al [12], Gamma-G (type 3) by Torabi and Montazari [13], Log-gamma-G by Amini et al [14], Exponentiated T-X by Alzaghal et al [15], Exponentiated-G (EG) by Cordeiro et al [16], Weibull-X by Alzaatreh et al [17], Weibull-G by Bourguignon et al [18], Logistic-G by Torabi and Montazari [19], Gamma-X by Alzaatreh et al [20], a Lomax-G family by Cordeiro et al [21], a new generalized Weibull-G family by Cordeiro et al [22], a Beta Marshall-Olkin family of distributions by Alizadeh et al [23], Logistic-X by Tahir et al [24], a new Weibull-G family by Tahir et al [25], a Lindley-G family by Cakmakyapan and Ozel [26], a Gompertz-G family by Alizadeh et al [27] and Odd Lindley-G family by Gomes-Silva et al [28] and so on.…”

Smooth Tests of Fit for the Lindley Distribution

“…Its motivation arises from its ability to model failure data with increasing, decreasing, unimodal, and bathtub-shaped hazard rates. See [2]. Ghitany et al [3] give many properties of the Lindley distribution.…”