Multi-stage point estimation of the mean of an inverse Gaussian distribution

Abstract

In this article, we develop two-stage, three-stage, and accelerated sequential procedures for the point estimation of the mean μ of an inverse Gaussian distribution when the scale parameter λ is unknown. Both minimum risk and bounded risk estimation problems are considered subject to a weighted squared error loss function. We aim at controlling the associated risk functions for all three procedures. Second-order approximations are obtained for the proposed procedures.

Keywords:

• Accelerated sequential procedure
• bounded risk
• fatigue life
• inverse Gaussian
• minimum risk
• point estimation
• second-order approximations
• three-stage procedure
• two-stage procedure

SUBJECT CLASSIFICATIONS:

• 62L12
• 62L05
• 62F12
• 62P30

Acknowledgments

The authors sincerely thank the anonymous referee, Associate Editor and Editor for their valuable comments and suggestions.