Two-stage and sequential procedures for estimation of powers of parameter of a family of distributions

Abstract

For the generalized positive exponential family of distributions, the problems of confidence interval estimation, bounded risk point estimation, and minimum risk point estimation of the rth power of unknown parameter θ are handled. Two-stage and purely sequential methodologies are developed for the estimation purpose. Sequential procedures are developed based on the maximum likelihood estimator (MLE) of the parameter. The exact operating characteristics of these procedures are given.

Keywords:

• Bounded risk
• confidence interval estimation
• generalized positive exponential family
• minimum risk
• point estimation

SUBJECT CLASSIFICATIONS:

• 62L10
• 62N05

ACKNOWLEDGMENT

The authors are grateful to the Editor-in-Chief, Professor Nitis Mukhopadhyay, for his valuable suggestion to add the minimum risk problem in this article, leading to an improved presentation.

DISCLOSURE

The authors have no conflicts of interest to report.

Additional information

Funding

Neeraj Joshi is grateful to the Department of Science and Technology, Government of India for their financial support (INSPIRE fellowship IF170889, 2018) in pursuing his research.