ON THE ESTIMATION OF ORDERED MEANS OF TWO EXPONENTIAL POPULATIONS

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 λ_{i}. The maximum likelihood estimator λ_{i}^{∗} of λ_{i} is shown to have a smaller mean square error than that of the usual estimator X̄_{i}, for each i = 1, 2. The asymptotic efficiency of λ_{i}^{∗} relative to X̄_{i} has also been found.

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