Computation and estimation of reliability for some bivariate copulas with Pareto marginals

In this article, we consider an expression for the probability , where X and Y are random variables denoting the strength and stress respectively. We assume that X and Y follow two-parameter Pareto distributions and model their dependency by a copula with the dependency parameter θ. We obtain expres...

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Bibliographic Details
Published in:Journal of statistical computation and simulation 2017-12, Vol.87 (18), p.3563-3589
Main Authors: Patil, Dipak D., Naik-Nimbalkar, U. V.
Format: Article
Language:English
Subjects:
Bivariate analysis
Blomqvist's beta
Computer simulation
Estimates
Gaussian error function
hypergeometric function
Method of moments
Monte Carlo method
Parameter estimation
Pareto optimum
ProductLog function
Random variables
stress-strength models
two-stage estimation procedure
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Summary:In this article, we consider an expression for the probability , where X and Y are random variables denoting the strength and stress respectively. We assume that X and Y follow two-parameter Pareto distributions and model their dependency by a copula with the dependency parameter θ. We obtain expression for R for four copula functions. We estimate R by plugging in the estimates of the marginal parameters and θ in its expression. The estimates of the marginal parameters are based on the marginal likelihoods. The estimates of θ are obtained from two different methods: one is based on the conditional likelihood and the other on the method of moments using Blomqvist's beta. Results of a simulation study show that the estimates based on Blomqvist's beta are better. We plot the graph of R versus θ to study the effect of dependency on R.
ISSN:0094-9655
1563-5163
DOI:10.1080/00949655.2017.1376328