Estimation of the Weibull parameters by Kullback-Leibler divergence of Survival functions

Yari, Gholamhossein; Mirhabibi, A.R.; Saghafi, Abolfazl

doi:10.12785/amis/070123

Cited by 12 publications

(15 citation statements)

References 13 publications

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“…Lee and Park [23] considered estimation of the Kullback-Leibler divergence between the true density and a selected parametric model. Yari et al [26] used the new divergence measure, called Kullback-Leibler divergence of Survival functions, to estimate the parameters of a Weibull distribution. The following definitions are available in [26].…”

Section: Introductionmentioning

confidence: 99%

“…Yari et al [26] used the new divergence measure, called Kullback-Leibler divergence of Survival functions, to estimate the parameters of a Weibull distribution. The following definitions are available in [26]. Definition 1.1.…”

Section: Introductionmentioning

confidence: 99%

“…Also the following theorems are available in [26] and hence the proof of theorems are not presented here. Theorem 1.3.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic reliability evaluation for a multi-state component under stress-strength model

Çalik¹

2017

J. Nonlinear Sci. Appl.

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For many technical systems, stress-strength models are of special importance. Stress-strength models can be described as an assessment of the reliability of the component in terms of X and Y random variables where X is the random "stress" experienced by the component and Y is the random "strength" of the component available to overcome the stress. The reliability of the component is the probability that component is strong enough to overcome the stress applied on it. Traditionally, both the strength of the component and the applied stress are considered to be both time-independent random variables. But in most of real life systems, the status of a stress and strength random variables clearly change dynamically with time. Also, in many important systems, it is very necessary to estimate the reliability of the component without waiting to observe the component failure. In this paper we study multi-state component where component is subjected to two stresses. In particular, inspired by the idea of Kullback-Leibler divergence, we aim to propose a new method to compute the dynamic reliability of the component under stress-strength model. The advantage of the proposed method is that Kullback-Leibler divergence is equal to zero when the component strength is equal to applied stress. In addition, the formed function can include both stresses when two stresses exist at the same time. Also, the proposed method provides a simple way and good alternative to compute the reliability of the component in case of at least one of the stress or strengths quantities depend on time.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic reliability evaluation for a multi-state component under stress-strength model

Çalik¹

2017

J. Nonlinear Sci. Appl.

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“…Teymori and Gupta (2012) introduce a point estimator for shape parameter of upper record Weibull distribution and use maximum-likelihood estimation (MLE) of scale parameter in their method. Also some inferential statistics based on Weibull distribution have been discussed by Yari and Saghafi (2012) and Yari et al (2013).…”

Section: Introductionmentioning

confidence: 99%

“…For estimation α the results show moment method estimation (MME) or KullbackLeibler divergence of survival function estimation (DLS) of β are better than maximum-likelihood estimation (MLE) of β. Now we introduce some basic definitions that play a central role in the present paper, using the notation of Wuu (2006), Cover and Thomass (2006) and Yari et al (2013).…”

Section: Introductionmentioning

confidence: 99%

Some Statistical Inferences on the Parameters of Records Weibull Distribution Using Entropy

Yari¹,

Rezaei²

2015

JSRI

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Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis

2022

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Estimation of the Weibull parameters by Kullback-Leibler divergence of Survival functions

Cited by 12 publications

References 13 publications

Dynamic reliability evaluation for a multi-state component under stress-strength model

Dynamic reliability evaluation for a multi-state component under stress-strength model

Some Statistical Inferences on the Parameters of Records Weibull Distribution Using Entropy

Relation between Relative Hazard Rates and Residual Divergence with some Applications to Reliability Analysis

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