Improved Estimators of the Hazard Rate from a Selected Gamma Population Under an Asymmetric Loss
Tóm tắt
We consider the problem of estimation of the hazard rate from a selected gamma population. Let
$$\Pi _{1}$$
,
$$\Pi _{2}$$
be two populations, where
$$\Pi _{i}$$
follows an one parameter gamma distribution with hazard rate
$$\lambda _{i}$$
,
$$i=1,2$$
. Let
$$ X_{i1},X_{i2},\ldots ,X_{in}$$
be an independent random sample drawn from the population
$$\Pi _{i}$$
,
$$i=1,2$$
. Consider
$$ X_{i}={\sum _{j=1}}^{n}X_{ij} $$
to be the sample mean of the ith population The natural selection rule is to select the population with largest(smallest) mean. That is
$$\Pi _{i}$$
if
$$X_{i}=max(min)(X_{1},X_{2})$$
. Some natural estimator are proposed and it was shown that they are admissible within a class of estimators with respect to the entropy loss. Further some improved estimators are obtained which improves upon the natural estimators.
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