Sankhya: The Indian Journal of Statistics

2003, Volume 65, Pt. 1, 91--106

Estimation Of Probabilities Of Linear Inequalities For Independent Elliptic Random Vectors


Marianna Pensky, University Of Central Florida, Usa

SUMMARY. The goal of  the present paper is to derive the  maximum likelihood estimators of probabilities   $\paxbycf$ where independent  vectors $\bX$ and $\bY$ have elliptical distributions. Also,  a  technique of Bayesian estimation is  proposed which enables one to avoid high-dimensional integration and, also,  to utilize results of Bayesian analysis conducted earlier. Estimators for familiar classes of elliptical distributions are constructed.

AMS (1991) subject classification. Primary 62H12; secondary 60E15, 62F15.

Key words and phrases. The stress-strength model,  elliptical distributions, maximum likelihood estimation, Bayes estimation.

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