Interval Estimation for the Stress-Strength Reliability with Bivariate Normal Variables

Pierre Nguimkeu; Marie Rekkas; Augustine Wong

doi:10.4236/ojs.2014.48059

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OJS> Vol.4 No.8, September 2014

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Interval Estimation for the Stress-Strength Reliability with Bivariate Normal Variables

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DOI: 10.4236/ojs.2014.48059 2,667 Downloads 3,367 Views Citations

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Pierre Nguimkeu¹, Marie Rekkas², Augustine Wong³

Affiliation(s)

¹Department of Economics, Georgia State University, Atlanta, GA, USA.
²Department of Economics, Simon Fraser University, Burnaby, Canada.
³Department of Mathematics and Statistics, York University, Toronto, Canada.

ABSTRACT

We propose a procedure to obtain accurate confidence intervals for the stress-strength reliability R = P (X > Y) when (X, Y) is a bivariate normal distribution with unknown means and covariance matrix. Our method is more accurate than standard methods as it possesses a third-order distributional accuracy. Simulations studies are provided to show the performance of the proposed method relative to existing ones in terms of coverage probability and average length. An empirical example is given to illustrate its usefulness in practice.

KEYWORDS

Bivariate Normal Distribution, Interval Estimation, Likelihood Analysis, Reliability

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Nguimkeu, P. , Rekkas, M. and Wong, A. (2014) Interval Estimation for the Stress-Strength Reliability with Bivariate Normal Variables. Open Journal of Statistics, 4, 630-640. doi: 10.4236/ojs.2014.48059.

References

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