Equivariant estimation for the parameters of location-scale multivariate exponential models and its application in reliability analysis

ABSTRACT

By considering an absolutely continuous location-scale multivariate exponential model (Weier and Basu, 1980), we obtain minimum risk equivariant estimator(s) of the parameter(s). Given a location-scale multivariate exponential random vector, it is shown that the normalized spacings associated with the random vector are independent standard exponential. The distribution of the complete sufficient statistic is derived. We derive the performance measures of standby, parallel, and series systems and also obtain the minimum risk equivariant estimator of the mean time before failure of the three systems. Some of the results of this article are extensions of those of Chandrasekar and Sajesh (2010).

Keywords:

• Equivariant
• Location-scale
• Multivariate exponential
• Reliability measures

Acknowledgment

The authors are grateful to an associate editor and a referee for their valuable suggestions which resulted in a substantial improvement of an earlier version of the paper. Thanks are due to the referee for bringing Brewster and Zidek (1974) and Kubokawa (1994) references to our attention and suggesting the improved estimator in Section 4.2.