The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data

Sharma, Vikas Kumar; Singh, Sanjay Kumar; Singh, Umesh; Agiwal, Varun

doi:10.1080/21681015.2015.1025901

Cited by 136 publications

(98 citation statements)

References 21 publications

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“…Por exemplo, a distribuição Lindley inversa, proposta por Sharma et al (2015a), é obtida a partir do inverso de uma variável aleatória com distribuição Lindley. Matematicamente, se uma variável aleatória Y tem distribuição Lindley então a variável aleatória X = Y −1 tem distribuição Lindley inversa com funções densidade, de distribuição acumulada e de risco definidas, respectivamente, por Outra generalização, proposta por Ghitany et al (2013) e nomeada de distribuição Lindley potência, considera a potência de uma variável aleatória com distribuição Lindley, ou seja X = Y 1 α em que α > 0.…”

Section: Introductionunclassified

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A distribuição Lindley potência inversa: diferentes métodos de estimação

Menezes

Mazucheli

Barco³

2018

CeN

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Resumo Nos últimos anos diversas distribuições de probabilidade foram propostas na literatura com propósitos de se obter funções densidade e de risco mais flexíveis. Por exemplo, Ghitany et al. (2013) propuseram uma generalização da distribuição Lindley e a nomearam de distribuição Lindley potência enquanto que Sharma et al. (2015a) propuseram a distribuição Lindley inversa. A partir destas duas generalizações, Barco et al. (2017) estudaram a distribuição Lindley potência inversa, também chamada por Sharma et al. (2015b) AbstractIn the last years several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible relative to the behaviors of the density and hazard rate functions. For instance, Ghitany et al. (2013) proposed a new generalization of the Lindley distribution, called power Lindley distribution, whereas Sharma et al. (2015a) proposed the inverse Lindley distribution. From these two generalizations Barco et al. (2017) studied the inverse power Lindley distribution, also called by Sharma et al. (2015b) as generalized inverse Lindley distribution. Considering the inverse power Lindley distribution, in this paper is evaluate the performance, through Monte Carlo simulations, with respect to the bias and consistency of nine different methods of estimations (the maximum likelihood method and eight others based on the distance between the empirical and theoretical cumulative distribution function

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Section: Introductionunclassified

“…Por exemplo, Ghitany et al (2013) propuseram uma generalização da distribuição Lindley e a nomearam de distribuição Lindley potência enquanto que Sharma et al (2015a) propuseram a distribuição Lindley inversa. A partir destas duas generalizações, Barco et al (2017) estudaram a distribuição Lindley potência inversa, também chamada por Sharma et al (2015b) …”

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A distribuição Lindley potência inversa: diferentes métodos de estimação

Menezes

Mazucheli

Barco³

2018

CeN

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“…Inverse Lindley (IL) distribution, proposed by Sharma et al [13], is a special case of the LW class with (7) and (8), Figure 4 shows the pdf and hrf of the IL distribution for some choices of . …”

Section: Inverse Lindley Distributionmentioning

confidence: 99%

A Class of Lindley and Weibull Distributions

Alkarni¹

2016

OJS

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In this paper, we introduce a class of Lindley and Weibull distributions (LW) that are useful for modeling lifetime data with a comprehensive mathematical treatment. The new class of generated distributions includes some well-known distributions, such as exponential, gamma, Weibull, Lindley, inverse gamma, inverse Weibull, inverse Lindley, and others. We provide closed-form expressions for the density, cumulative distribution, survival function, hazard rate function, moments, moments generating function, quantile, and stochastic orderings. Moreover, we discuss maximum likelihood estimation and the algorithm for computing the parameters estimates. Some sub models are discussed as an illustration with real data sets to show the flexibility of this class.

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“…Many authors have proposed to use Lindley's approximation to obtain Bayes estimates of the parameters for various lifetime distributions and references cited (Sharma et al, 2015(Sharma et al, , 2016b. The ratio of integrals occurs in Bayesian analysis is given by 6) where Θ = {θ 1 , θ 2 , .…”

Section: Lindley's Approximationmentioning

confidence: 99%

Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data

Sharma

Singh

2017

CSAM

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The power Lindley distribution with some of its properties is considered in this article. Maximum likelihood, least squares, maximum product spacings, and Bayes estimators are proposed to estimate all the unknown parameters of the power Lindley distribution. Lindley's approximation and Markov chain Monte Carlo techniques are utilized for Bayesian calculations since posterior distribution cannot be reduced to standard distribution. The performances of the proposed estimators are compared based on simulated samples. The waiting times of research articles to be accepted in statistical journals are fitted to the power Lindley distribution with other competing distributions. Chi-square statistic, Kolmogorov-Smirnov statistic, Akaike information criterion and Bayesian information criterion are used to access goodness-of-fit. It was found that the power Lindley distribution gives a better fit for the data than other distributions.

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The inverse Lindley distribution: a stress-strength reliability model with application to head and neck cancer data

Cited by 136 publications

References 21 publications

A distribuição Lindley potência inversa: diferentes métodos de estimação

A distribuição Lindley potência inversa: diferentes métodos de estimação

A Class of Lindley and Weibull Distributions

Classical and Bayesian methods of estimation for power Lindley distribution with application to waiting time data

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