1
Southwest Jiaotong University Hope College, Chengdu 610400, China
2
Department of Statistics, Southwest Jiaotong University, Chengdu 611756, China
Abstract
This article explores Bayesian inference for the reliability of the binomial distribution in cases with zero-failure data. We propose Expected-Bayesian (E-Bayesian) and hierarchical Bayesian estimators of reliability, considering three different joint prior distributions of hyper-parameters in the prior distribution of reliability, which is assumed to follow a beta distribution. We derive closed-form expressions for the E-Bayesian estimators of reliability and propose hierarchical Bayesian estimators, which are subsequently evaluated using Monte Carlo simulations. Furthermore, we study the one-sided modified Bayesian (M-Bayesian) lower credible limits for reliability. The performance of the proposed methods is demonstrated through Monte Carlo simulations. Finally, a real data example is analyzed for illustrative purposes.
Jiang, Y., & Feng, X. (2024). Bayesian inference of reliability in the case of zero-failure data for the binomial distribution. Stochastic Models in Probability and Statistics, 1(2), 191-209.
MLA
Yuting Jiang; Xuefeng Feng. "Bayesian inference of reliability in the case of zero-failure data for the binomial distribution", Stochastic Models in Probability and Statistics, 1, 2, 2024, 191-209.
HARVARD
Jiang, Y., Feng, X. (2024). 'Bayesian inference of reliability in the case of zero-failure data for the binomial distribution', Stochastic Models in Probability and Statistics, 1(2), pp. 191-209.
VANCOUVER
Jiang, Y., Feng, X. Bayesian inference of reliability in the case of zero-failure data for the binomial distribution. Stochastic Models in Probability and Statistics, 2024; 1(2): 191-209.
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