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.