Lindley distribution and its application

Ghitany, M. E.; Atieh, B.; Nadarajah, Saralees

doi:10.1016/j.matcom.2007.06.007

Cited by 643 publications

(398 citation statements)

References 5 publications

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“…To generate random Lindley values, we follow [3] and observe that the Lindley distribution is a mixture of an exponential (θ) distribution and a gamma (2, θ) distribution. To obtain a random x value we need four uniform (0, 1) values, u 1 , u 2 , u 3 and u 4 say, and take x = −{log(u 1 u 2 )}/θ unless u 4 ≤ θ/(θ + 1), in which case x = −(log u 3 )/θ.…”

Section: The Approach To the Asymptotic Distributionmentioning

confidence: 99%

“…Waiting Time Data. Ghitany [3] gives the waiting times (in minutes) before service of 100 bank customers. On the basis of a superior log likelihood they conclude that the Lindley distribution gives a better fit than the exponential.…”

Section: Examplesmentioning

confidence: 99%

“…See [2]. Ghitany et al [3] give many properties of the Lindley distribution. They suggest it is often a better model than the traditional exponential distribution that is commonly used to model lifetime or waiting time data.…”

Section: Introductionmentioning

confidence: 99%

“…Ghitany et al [3] examine the fit of the Lindley distribution to some waiting time data by looking at plots and by showing the Lindley likelihood is better than the exponential likelihood. However, this does not demonstrate that the Lindley distribution fits the data well, only that it fits better than the exponential.…”

Section: Introductionmentioning

confidence: 99%

“…It is suggested that p-values be found using the parametric bootstrap. A slightly expanded version of an algorithm in Ghitany et al [3] generating random Lindley variates is given in Section 3 so that these p-values can be calculated. Some powers of the smooth test and the Anderson-Darling test are compared in Section 4 while Section 5 gives two examples.…”

Section: Introductionmentioning

confidence: 99%

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Smooth Tests of Fit for the Lindley Distribution

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Rayner

2018

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Abstract:We consider the little-known one parameter Lindley distribution. This distribution may be of interest as it appears to be more flexible than the exponential distribution, the Lindley fitting more data than the exponential. We give smooth tests of fit for this distribution. The smooth test for the Lindley has power comparable with the Anderson-Darling test. Advantages of the smooth test are discussed. Examples that illustrate the flexibility of this distributions is given.

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Section: The Approach To the Asymptotic Distributionmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Smooth Tests of Fit for the Lindley Distribution

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Rayner

2018

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Comparing estimation of the parameters of distribution of the root density of plants in the presence of outliers

Nooghabi

2021

Environmetrics

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The root density of plants with depth follows exponential or the Lindley distribution in the presence of outliers generated from a uniform distribution. In this article, we estimate the parameters of the Lindley distribution in the presence of outliers generated from a uniform distribution based on the moment, maximum likelihood, least squares, weighted least squares, percentile, Cramer-von-Mises, and Anderson-Darling methods and mixture estimator of moment and maximum likelihood. These methods of estimation are compared. Also, the estimators of the parameters of Lindley-uniform contaminated distribution are compared with the corresponding estimators of exponential-uniform contaminated distribution, which was presented by Dixit and Nasiri, Metron, 59(3-4), 187-198 (2001). Furthermore, an analysis of an actual example of the root length of plants is presented for illustrative purposes. It is concluded that the Lindley-uniform contaminated distribution is more appropriate than the exponential-uniform contaminated distribution to model the root density of plants.

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On estimation procedures of constant stress accelerated life test for generalized inverse lindley distribution

Kumar

Nassar

Dey³

et al. 2021

Quality & Reliability Eng

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In manufacturing industries and several other fields, accelerated life testing is used widely to obtain sufficient failure time data of test units quickly as compared to normal use conditions. It is assumed that the lifetime of a product at constant stress level follows generalized inverse Lindley distribution. It is a common observation that while estimating the parameters of a model, one usually adopts the maximum likelihood estimation method as the starting point. In this paper, we consider eight frequentist methods of estimation, besides using the maximum likelihood method for estimating the parameters of the generalized inverse Lindley distribution under constant stress accelerated life test. In addition, the shape parameter and the reliability function of the model under usual conditions are obtained using nine considered estimation methods. Monte Carlo simulations are performed for investigating the performances of the considered methods in terms of their mean relative estimates and mean square errors using small, medium and large sample sizes. One accelerated life test data set is analyzed for illustrative purposes. In addition, bootstrap confidence intervals of the parameters are obtained as part of data analysis based on the considered estimation methods.

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Lindley distribution and its application

Cited by 643 publications

References 5 publications

Smooth Tests of Fit for the Lindley Distribution

Smooth Tests of Fit for the Lindley Distribution

Comparing estimation of the parameters of distribution of the root density of plants in the presence of outliers

On estimation procedures of constant stress accelerated life test for generalized inverse lindley distribution

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