Exact Risks of Sequential Point Estimators of the Exponential Parameter

Abstract

Under purely sequential sampling schemes, a theory is developed for the exact determination of the distributions of two classes of stopping variables (rules) in order to handle point estimation problems for the parametric functionals in an exponential distribution. Explicit formulae are derived for the expected value and risks of sequential estimators of the mean, failure rate, and reliability function of an exponential distribution. These are utilized to compare performances of several competing estimators of the mean and the failure rate.

Recommended by Ben Boukai

Keywords:

• Exponential distribution
• Point estimators
• Sequential procedures
• Stopping variables

Subject Classifications:

• 62L05
• 62L12

ACKNOWLEDGMENTS

The authors are most grateful to the associate editor and the referees for their comments. We also acknowledge Professors Robert V. Hogg and E. A. Tanis for permission to use waiting-time data from their 2005 book.

Notes

Recommended by Ben Boukai