Estimation Of Several Samples Exponential Distributions Under Simple Tree Order

The present paper deals with the estimation of the means of several samples exponential distributions, with the different sample size under Simple Tree Order.In charter 2, the maximum likelihood estimator is given in this paper with the different sample size under Simple Tree Order (λ₀≤λ_i, (i=1, 2, 3.. n)).In charter 3, Let X_i, i=1, 2, 3 be the observations from three exponential distributions with unknown meansλ_i. From experience, we may assume that there are some order restrictions among the means, for example, simple tree order restrictions(λ₁≤min(λ₂,λ₃)). We discuss the means of three sample exponential distributions, with the same sample size, under Simple Tree Order. It shows that:1.λ₂=λ₃: the restricted maximum likelihood estimators (RMLE) have less mean square errors than the usual sample means.2.λ₂≠λ₃:1) X₁≤minmin(X_2, X₃):the restricted maximum likelihood estimators (RMLE) have equal mean square errors with the usual sample means.2) X₂＜X₁: the restricted maximum likelihood estimators (RMLE) have less mean square errors than the usual sample means.3) X₃＜X₁: the restricted maximum likelihood estimators (RMLE) have less mean square errors than the usual sample means.4)max(X₂,X₃)≤X₁:λ₂≠λ₃ use the result with experiment we can't tell which of the restricted maximum likelihood estimators (RMLE) and usual sample means have less mean square errors...