Bounded risk estimation of the hazard rate function of the exponential distribution: Two-stage procedure

ABSTRACT

In this article, we consider sequential point estimation of hazard rate function of an exponential distribution () subject to the risk function given as , where 0<A<∞ and ω>0 are known constants. We provide explicit formulas for the distribution of the total sample size, N_m, and of the expected value and risk of the estimator of the hazard rate function of the exponential distribution. In addition, we propose how to determine the parameter K( = K(m,A)) of the stopping variable N_m so that the risk is uniformly bounded by ω. In the end, the performances of the proposed methodology are investigated with the help of simulations and two applied examples.

KEYWORDS:

• Bounded risk estimation
• exact distribution
• exponential distribution
• hazard rate function
• sequential estimation
• stopping variables
• two-stage procedure

MATHEMATICS SUBJECT CLASSIFICATION:

• 62L15
• 60G40
• 62F12
• 62F15

Acknowledgments

The authors are grateful to the Editor-in-Chief, Professor Nitis Mukhopadhyay, and an associate editor and the referee(s) for their valuable comments, which led to an improvements in the article. We thank the publisher, Springer, for giving us permission to use data for our illustration(s). The authors are also indebted to Yazd University for supporting this research.