A new modified Lindley distribution with properties and applications

Chesneau, Christophe; Tomy, Lishamol; Gillariose, Jiju

doi:10.1080/09720510.2020.1824727

Cited by 14 publications

(19 citation statements)

References 19 publications

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“…Recently, Chesneau et al [ 6 ] have introduced a general family of Lindley, called modified Lindley (ML) distribution based on the use of a new tuning function, which aims at modulating the polynomial term in the definition of the cdf given by ( 1 ). The cdf and pdf of the ML distribution are given by

…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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A two-parameter continuous distribution, namely, power-modified Lindley (PML), is proposed. Various structural properties of the new distribution, including moments, moment-generating function, conditional moments, mean deviations, mean residual lifetime, and mean past lifetime, are provided. The reliability of a system is discussed when the strength of the system and the stress imposed on it are independent. Maximum-likelihood estimation of the parameters and their estimated asymptotic standard errors are derived. Bayesian estimation methods of the parameters with independent gamma prior are discussed based on symmetric and asymmetric loss functions. We proposed using the MCMC technique with the Metropolis–Hastings algorithm to approximate the posteriors of the stress-strength parameters for Bayesian calculations. The confidence interval for likelihood and the Bayesian estimation method is obtained for the parameter of the model and stress-strength reliability. We prove empirically the importance and flexibility of the new distribution in modeling with real data applications.

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…”

Section: Introductionmentioning

confidence: 99%

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Al-Babtain

Elbatal

Almetwally

2022

Computational Intelligence and Neuroscience

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“…Among which the modified Lindley (ML) distribution developed by Chesneau 5 is of prime importance. Suppose Y is a random variable following the ML distribution with parameter , then the pdf of ML distribution is defined as follows ( ) ( )…”

Section: Introductionmentioning

confidence: 99%

A comparative study of various estimation methods for modified Lindley distribution

Veena¹,

Tomy²

2022

BBIJ

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The purpose of this study is to examine the finite sample aspects of estimates of the parameters of the weighted Lindley distribution derived by four estimation methods: maximum likelihood, method of moments, ordinary least squares, and weighted least squares, using Monte Carlo simulations. As a comparison criterion, bias and mean-squared error are used. In both small and large samples, the Cramer-von Mises approach is found to be very competing with the maximum likelihood method. To substantiate the conclusion, a statistical analysis of a real data set related to weather is performed.

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“…In this research, we contribute to the developments of the S-G family by linking it to a particular one-parameter distribution introduced by [11]: the modified Lindley (ML) distribution. The sine ML (S-ML) distribution is thus introduced.…”

Section: Introductionmentioning

confidence: 99%

“…In order to comprehend the outlined approach, a review of the ML distribution is essential. As a first comment, the ML distribution presented by [11] is achieved by implementing the tuning exponential function e −θx , with θ > 0, to the Lindley distribution, with the motive of modifying its capabilities for new modeling perspectives. On the mathematical side, the cdf and pdf of the ML distribution are defined by…”

Section: Introductionmentioning

confidence: 99%

“…The ML distribution is also identified as a linear combination of the exponential distribution with parameter θ and the gamma distribution with parameters (2, 2θ), and it has an "increasing-reverse bathtub-constant" hazard rate function (hrf). The real benefit is quite noteworthy; the ML model is superior to the Lindley and exponential models for the three data sets seen in [11]. A few inspired distributions enhancing or generalising the ML distribution were proposed for the purpose of optimality.…”

Section: Introductionmentioning

confidence: 99%

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The Sine Modified Lindley Distribution

Tomy¹,

Veena²,

Chesneau

2021

MCA

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The paper contributes majorly in the development of a flexible trigonometric extension of the well-known modified Lindley distribution. More precisely, we use features from the sine generalized family of distributions to create an original one-parameter survival distribution, called the sine modified Lindley distribution. As the main motivational fact, it provides an attractive alternative to the Lindley and modified Lindley distributions; it may be better able to model lifetime phenomena presenting data of leptokurtic nature. In the first part of the paper, we introduce it conceptually and discuss its key characteristics, such as functional, reliability, and moment analysis. Then, an applied study is conducted. The usefulness, applicability, and agility of the sine modified Lindley distribution are illustrated through a detailed study using simulation. Two real data sets from the engineering and climate sectors are analyzed. As a result, the sine modified Lindley model is proven to have a superior match to important models, such as the Lindley, modified Lindley, sine exponential, and sine Lindley models, based on goodness-of-fit criteria of importance.

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A new modified Lindley distribution with properties and applications

Cited by 14 publications

References 19 publications

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

Bayesian and Non-Bayesian Reliability Estimation of Stress-Strength Model for Power-Modified Lindley Distribution

A comparative study of various estimation methods for modified Lindley distribution

The Sine Modified Lindley Distribution

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