Sequential bounded risk point estimation of parameters of a negative exponential distribution

Abstract

In this paper we consider the probier11 of estirrlatiiig with given constants a and b > 0, based on t,he sample from an exponentiai distribution with location and scale pararrleters µ and δ. both unknov:n. For a preassigned quantity w > 0 we want to estimate θby using the sampie of the smallest size such that the risk associated with an estimator is not greater than w. We propose an estimator and a slight more general class of estimators and define a stopping rule. The asymptotic expansions of the risks associated wit11 these estimators are obtained. \le also compare them from the point of view of risk.

Keywords:

• Two-Parameter exponetial
• bounded risk
• Asymptotic expsansion
• uniform integrability

Additional information

Notes on contributors

Eiichi Isogai

Kazumasa Saito

2

Chikara Uno

3