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SEQUENTIAL ESTIMATION OF A PARAMETER OF

AN EXPONENTIAL DISTRIBUTION

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EIICHI ISOGAI AND CHIKARA UNO

*Department of Mathematics, Niigata University, 8050 Ikarashi
2-cho, Niigata 950-21, Japan*
(Received June 19, 1992; revised November 9, 1992)

**Abstract.**
We consider the problem of minimum risk point
estimation for the parameter *theta* = *a**mu*+*b**sigma* of the exponential
distribution with unknown location parameter *mu* and scale parameter
*sigma* when the loss function is squared error plus linear cost. In this
paper, we propose a sequential estimator of *theta* and show that the
associated risk is asymptotically one cost less than that given by Ghosh
and Mukhopadhyay (1989, *South African Statist. J.*, **23**,
251-268).

*Key words and phrases*:
Two-parameter exponential,
asymptotically unbiased estimator, sequential estimator, uniform
integrability, second order.

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