Stress and Strength Reliability Estimation for the Inverse Family of Distributions using Bayesian Analysis
DOI:
https://doi.org/10.13052/jrss0974-8024.1921Keywords:
Inverse family of distributions, stress-strength model, Bayesian estimation, squared error loss function, general entropy loss function, reliability function, bootstrapAbstract
A Bayesian model to study stress-strength reliability P=P(Y<X), which makes use of parameters in the family of the inverse distributions. For the reliability function and for the stress-strength parameter, Bayes estimators are obtained under SELF and GELF. When this is appropriate, conjugate priors will be introduced into estimators, which will be constituted using different powers of the unknown parameters. Performance of these estimators is determined by a simulation-based methodology and large numbers of bootstrap replications. The findings show that, especially in small-sample circumstances, the Bayesian estimators based on SELF perform better than those based on GELF. The performance difference closes as the sample sizes grow. The exploration of this paper displays that the inverse family can be altered for several common distributions, which have more significant practical implications when analyzing reliability.
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