Sequential fixed-width confidence interval for the rth power of the exponential scale parameter: Two-stage and sequential sampling procedures

Abstract

In this paper, we study two-stage and sequential sampling procedures for estimating the rth power of the exponential scale parameter, i.e., β^r, where the fixed-width confidence interval is considered. The exact operating characteristics of sequential procedures for fixed-width, $2\delta$ ($\delta >0$), confidence interval estimation is given. We show that the results of Zacks (2009), for two-stage and sequential procedures, can be deduced from our general results.

KEYWORDS:

• Fixed-width confidence intervals
• Regular Poisson process
• Sequential estimation
• Stopping variable
• Two-stage sampling procedure

Subject Classifications:

• 62L10
• 62N05

Acknowledgments

The authors are grateful to the Editor-in-Chief, Professor Nitis Mukhopadhyay, an Associate editor and the referee(s) for their valuable comments. The authors are also indebted to Yazd University for supporting this research.