Volume 8, Issue 1 And 2 (November 2009)
JIRSS 2009, 8(1 And 2): 15-34 |
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Meghnatisi Z, Nematollahi N. Mixed Estimators of Ordered Scale Parameters of Two Gamma Distributions with Arbitrary Known Shape Parameters. JIRSS. 2009; 8 (1 and 2) :15-34
URL: http://jirss.irstat.ir/article-1-74-en.html
URL: http://jirss.irstat.ir/article-1-74-en.html
Abstract: (9286 Views)
When an ordering among parameters is known in advance,
the problem of estimating the smallest or the largest parameters
arises in various practical problems. Suppose independent random
samples of size ni drawn from two gamma distributions with
known 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 restriction 0 < beta_1 < beta_ 2. It has been shown that a subclass of mixed estimators of i, beats the usual estimators frac{bar{X_i}}{nu_i}, i = 1, 2, and a class of admissible estimators in the class of mixed estimators are derived under scale-invariant squared error loss function. Also it has been shown that the mixed estimator of 0
the problem of estimating the smallest or the largest parameters
arises in various practical problems. Suppose independent random
samples of size ni drawn from two gamma distributions with
known 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 restriction 0 < beta_1 < beta_ 2. It has been shown that a subclass of mixed estimators of i, beats the usual estimators frac{bar{X_i}}{nu_i}, i = 1, 2, and a class of admissible estimators in the class of mixed estimators are derived under scale-invariant squared error loss function. Also it has been shown that the mixed estimator of 0
Keywords: Admissibility, mixed estimators, ordered parameters, scale-invariant squared error loss function, simultaneous estimation.
Subject:
60: Probability theory and stochastic processes
Received: 2011/08/9 | Accepted: 2015/09/12
Received: 2011/08/9 | Accepted: 2015/09/12
