### 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 lambdai. The maximum likelihood estimator lambdai* of lambdai is shown to have a smaller mean square error than that of the usual estimator \bar Xi, for each i = 1, 2. The asymptotic efficiency of lambdai* relative to \bar Xi has also been found.

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

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