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American Journal of Mathematical and Management Sciences Volume 37, 2018 - Issue 1
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Original Articles

Bayesian and Classical Estimation of the Inverse Pareto Distribution and Its Application to Strength-Stress Models

Lei GuoDepartment of Mathematics, Beijing Jiaotong University, Beijing, ChinaView further author information
&
Wenhao GuiDepartment of Mathematics, Beijing Jiaotong University, Beijing, ChinaCorrespondencewhgui@bjtu.edu.cn
View further author information
Pages 80-92 | Published online: 16 Oct 2017
 
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SYNOPTIC ABSTRACT

This article deals with the estimation of R = P(Y < X) when X and Y are two independent random variables following inverse Pareto distributions with different parameters. The maximum-likelihood estimator of R and its asymptotic sampling distribution are proposed. The asymptotic sampling distribution is used to construct an asymptotic confidence interval for R. The exact confidence interval and bootstrap confidence interval for R are also presented. Bayes estimate and credible interval are studied using Gibbs sampling technique. Monte Carlo simulations are performed to compare the performance of different proposed estimation methods. Analysis of a real data set is presented for illustrative purposes.

Additional information

Funding

Wenhao Gui’s work was partially supported by the program for the Fundamental Research Funds for the Central Universities (No. 2014RC042).

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