Inference for the Johnson S_B distribution

Abstract

This article develops inferential procedures for the Johnson S_B distribution and the associated stress-strength model. The maximum likelihood estimators, uniformly minimum variance unbiased estimators and generalized confidence intervals for the parameters of the Johnson S_B distribution are presented. The objective Bayesian inference methods based on the Jeffreys and reference priors are derived. Moreover, the generalized confidence lower limits and Bayesian credible lower limits for the reliability of the stress-strength model are provided. The performance of the proposed methods is evaluated by Monte Carlo simulation. Finally, an example is used to illustrate the proposed procedures.

Keywords:

• Generalized inference
• Johnson S_B distribution
• Objective Bayesian
• Stress-strength model

Acknowledgments

The authors would like to thank the editors and referees for their valuable suggestions, which have greatly improved this article.

Additional information

Funding

The work is supported by the National Natural Science Foundation of China (Grant Nos. 12271480, 12171432), the characteristic & preponderant discipline of key construction universities in Zhejiang Province (Zhejiang Gongshang University- Statistics) and the Collaborative Innovation Center of Statistical Data Engineering.