Objective Bayesian analysis of JM model in software reliability

Yongqiang Lian; Yincai Tang; Yijun Wang

doi:10.1016/j.csda.2016.12.006

Objective Bayesian analysis of JM model in software reliability

Yongqiang Lian, Yincai Tang, Yijun Wang

School of Statistics

East China Normal University

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

Jelinski Moranda (JM) model is frequently used in software reliability. The objective Bayesian inference was proposed to estimate the parameters of JM model. Jeffreys prior and reference priors have been derived. Besides, the properties of corresponding posteriors were deduced and some modifications were made which made the posterior distributions proper. Then Gibbs sampling was utilized to obtain the Bayesian estimators, credible intervals and coverage probabilities of the parameters. Comparisons in the efficiency of the maximum likelihood estimators and Bayesian estimators under different priors for various sample sizes have been done by simulations and a real data set was analyzed for illustrative purpose.

Original language	English
Pages (from-to)	199-214
Number of pages	16
Journal	Computational Statistics and Data Analysis
Volume	109
DOIs	https://doi.org/10.1016/j.csda.2016.12.006
State	Published - 1 May 2017

Keywords

Gibbs sampling
Jeffreys prior
Objective Bayesian analysis
Probability matching prior
Reference prior
Software reliability

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10.1016/j.csda.2016.12.006

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title = "Objective Bayesian analysis of JM model in software reliability",

abstract = "Jelinski Moranda (JM) model is frequently used in software reliability. The objective Bayesian inference was proposed to estimate the parameters of JM model. Jeffreys prior and reference priors have been derived. Besides, the properties of corresponding posteriors were deduced and some modifications were made which made the posterior distributions proper. Then Gibbs sampling was utilized to obtain the Bayesian estimators, credible intervals and coverage probabilities of the parameters. Comparisons in the efficiency of the maximum likelihood estimators and Bayesian estimators under different priors for various sample sizes have been done by simulations and a real data set was analyzed for illustrative purpose.",

keywords = "Gibbs sampling, Jeffreys prior, Objective Bayesian analysis, Probability matching prior, Reference prior, Software reliability",

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year = "2017",

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AU - Lian, Yongqiang

AU - Tang, Yincai

AU - Wang, Yijun

PY - 2017/5/1

Y1 - 2017/5/1

N2 - Jelinski Moranda (JM) model is frequently used in software reliability. The objective Bayesian inference was proposed to estimate the parameters of JM model. Jeffreys prior and reference priors have been derived. Besides, the properties of corresponding posteriors were deduced and some modifications were made which made the posterior distributions proper. Then Gibbs sampling was utilized to obtain the Bayesian estimators, credible intervals and coverage probabilities of the parameters. Comparisons in the efficiency of the maximum likelihood estimators and Bayesian estimators under different priors for various sample sizes have been done by simulations and a real data set was analyzed for illustrative purpose.

AB - Jelinski Moranda (JM) model is frequently used in software reliability. The objective Bayesian inference was proposed to estimate the parameters of JM model. Jeffreys prior and reference priors have been derived. Besides, the properties of corresponding posteriors were deduced and some modifications were made which made the posterior distributions proper. Then Gibbs sampling was utilized to obtain the Bayesian estimators, credible intervals and coverage probabilities of the parameters. Comparisons in the efficiency of the maximum likelihood estimators and Bayesian estimators under different priors for various sample sizes have been done by simulations and a real data set was analyzed for illustrative purpose.

KW - Gibbs sampling

KW - Jeffreys prior

KW - Objective Bayesian analysis

KW - Probability matching prior

KW - Reference prior

KW - Software reliability

UR - https://www.scopus.com/pages/publications/85007574143

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DO - 10.1016/j.csda.2016.12.006

M3 - 文章

AN - SCOPUS:85007574143

SN - 0167-9473

VL - 109

SP - 199

EP - 214

JO - Computational Statistics and Data Analysis

JF - Computational Statistics and Data Analysis

ER -

Objective Bayesian analysis of JM model in software reliability

Abstract

Keywords

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