Estimating ordered quantiles of two exponential populations with a common minimum guarantee time

Abstract

The problem of estimating ordered quantiles of two exponential populations is considered, assuming equality of location parameters (minimum guarantee times), using the quadratic loss function. Under order restrictions, we propose new estimators which are the isotonized version of the MLEs, call it, restricted MLE. A sufficient condition for improving equivariant estimators is derived under order restrictions on the quantiles. Consequently, estimators improving upon the old estimators have been derived. A detailed numerical study has been done to evaluate the performance of proposed estimators using the Monte-Carlo simulation method and recommendations have been made for the use of the estimators.

Keywords:

• Equivariant estimators
• inadmissibility
• quadratic loss function
• quantile estimation
• relative risk performance
• ordered parameters

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F10
• 62C15

Acknowledgments

The authors thank an anonymous reviewer and the editor for their valuable suggestions and comments which have helped in improving the manuscript.