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ON THE ESTIMATION OF ORDERED MEANS OF

TWO EXPONENTIAL POPULATIONS

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AMARJOT KAUR AND HARSHINDER SINGH

*Department of Statistics, Panjab University, Chandigarh 160014, India*
(Received April 3, 1989; revised February 14, 1990)

**Abstract.**
Let random samples of equal sizes be drawn from
two exponential distributions with ordered means *lambda*_{i}. The
maximum likelihood estimator *lambda*_{i}^{*} of *lambda*_{i} is shown to
have a smaller mean square error than that of the usual estimator \bar *X*_{i},
for each *i* = 1, 2. The asymptotic efficiency of *lambda*_{i}^{*}
relative to \bar *X*_{i} has also been found.

*Key words and phrases*:
Asymptotic efficiency, exponential distribution,
isotonic regression, maximum likelihood estimation, mean square error.

**Source**
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