Two-stage procedures for the bounded risk point estimation of the parameter and hazard rate in two families of distributions

ABSTRACT

Two families of distributions are considered that cover a large number of probability distributions useful in investigations involving reliability studies and survival analyses. The problem of bounded risk point estimation of the parameter and hazard rate function of the two families of distribution is handled. Motivated by Mukhopadhyay and Pepe (2006), Roughani and Mahmoudi (2015), and Mahmoudi and Lalehzari (2017), two-stage procedures are developed based on the maximum likelihood estimator (MLE) as well as uniformly minimum variance unbiased estimator (UMVUE). The estimation problem based on the minimum mean square estimator (MMSE) is also considered. We establish that the MMSE of the parameter and hazard rate provides a smaller risk.

KEYWORDS:

• Bounded risk estimation
• exact distributions
• hazard rate
• Moore and Bilikam family of distributions
• sequential estimation
• simulations
• stopping variables
• two-stage sampling

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 62L12
• 62L05
• 62L15

Acknowledgments

We thank the Associate Editor and a reviewer for their helpful comments.