Sankhya: The Indian Journal of Statistics

1993, Volume 55, Series A, Pt. 2, 305-311

A SEQUENTIAL PROCEDURE FOR ESTIMATION OF ORDERED MEANS OF TWO EXPONENTIAL POPULATIONS

By

J. C. PARNAMI, HARSHINDER SINGH, *Panjab University*

SUMMARY. Let $X_i (Y_i)$ denote the $i$-th random observation from exponential distribution with mean $\mu_1 (\mu_2)$ where it is a priori known that $\mu_1\leq \mu_2$. Let $n_0$ be a fixed positive integer and $N$ be the smallest positive integer greater than or equal to $n_0$ such that $\sum_{i=1}^{N}X_i\leq \sum_{i=1}^{N}Y_i$. it has been established that with probability one $N$ is a finite valued random variable. expression for $E(N)$ has been found out. $1/N \sum_{i=1}^{N}X_i$ and $1/N \sum_{i=1}^{N}Y_i$ have been considered as estimators of $\mu_1$ and $\mu_2$ respectively and expressions for their first two moments have been obtained.

*AMS (1980) subject classification.* 62L12,62F30

*Key words and phrases*. Co-efficient of variation, mean square error, sequential procedure, statistical inference under order restrictions