Estimation of Linear Functions of Ordered Scale Parameters of Two Gamma Distributions under Entropy Loss
نویسندگان
چکیده
The problem of estimating linear functions of ordered scale parameters of two Gamma distributions is considered under entropy loss. A necessary and sufficient condition for the maximum likelihood estimator (MLE) to dominate the crude unbiased estimator (UE) is given on two non-negative coefficients. Furthermore, improvement on the UE of the reciprocal of each scale parameter is also obtained under entropy loss. Some numerical results are given to illustrate how much improvement is obtained over the UE.
منابع مشابه
Mixed Estimators of Ordered Scale Parameters of Two Gamma Distributions with Arbitrary Known Shape Parameters
When an ordering among parameters is known in advance,the problem of estimating the smallest or the largest parametersarises in various practical problems. Suppose independent randomsamples of size ni drawn from two gamma distributions withknown arbitrary shape parameter no_i > 0 and unknown scale parameter beta_i > 0, i = 1, 2. We consider the class of mixed estimators of 1 and 2 under the res...
متن کاملTruncated Linear Minimax Estimator of a Power of the Scale Parameter in a Lower- Bounded Parameter Space
Minimax estimation problems with restricted parameter space reached increasing interest within the last two decades Some authors derived minimax and admissible estimators of bounded parameters under squared error loss and scale invariant squared error loss In some truncated estimation problems the most natural estimator to be considered is the truncated version of a classic...
متن کاملBayesian Estimation of Shift Point in Shape Parameter of Inverse Gaussian Distribution Under Different Loss Functions
In this paper, a Bayesian approach is proposed for shift point detection in an inverse Gaussian distribution. In this study, the mean parameter of inverse Gaussian distribution is assumed to be constant and shift points in shape parameter is considered. First the posterior distribution of shape parameter is obtained. Then the Bayes estimators are derived under a class of priors and using variou...
متن کاملESTIMATION OF SCALE PARAMETER UNDER A REFLECTED GAMMA LOSS FUNCTION
In this paper, the estimation of a scale parameter t under a new and bounded loss function, based on a reflection of the gamma density function, is discussed. The best scale-invariant estimator of tis obtained and the admissibility of all linear functions of the sufficient statistic, for estimating t in the absence of a nuisance parameter, is investigated
متن کاملMinimax Estimation of the Scale Parameter in a Family of Transformed Chi-Square Distributions under Asymmetric Squared Log Error and MLINEX Loss Functions
This paper is concerned with the problem of finding the minimax estimators of the scale parameter ? in a family of transformed chi-square distributions, under asymmetric squared log error (SLE) and modified linear exponential (MLINEX) loss functions, using the Lehmann Theorem [2]. Also we show that the results of Podder et al. [4] for Pareto distribution are a special case of our results for th...
متن کامل