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  1. 3 Applicationes Mathematicae

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  1. 3 Sengupta S.

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  1. 2 2010

  2. 1 2009

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Unbiased estimation of reliability for two-parameter exponential distribution under time censored sampling

100%
Sengupta S.
Applicationes Mathematicae
|
2010
|
tom 37
|
nr 1
99-111
EN
The problem considered is that of unbiased estimation of reliability for a two-parameter exponential distribution under time censored sampling. We give necessary and sufficient conditions for the existence of uniformly minimum variance unbiased estimator and also provide a characterization of a complete class of unbiased estimators in situations where unbiased estimators exist.
2
Content available remote

Estimation of the size of a closed population

100%
Sengupta S.
Applicationes Mathematicae
|
2010
|
tom 37
|
nr 2
237-245
EN
The problem considered is that of estimation of the size (N) of a closed population under three sampling schemes admitting unbiased estimation of N. It is proved that for each of these schemes, the uniformly minimum variance unbiased estimator (UMVUE) of N is inadmissible under square error loss function. For the first scheme, the UMVUE is also the maximum likelihood estimator (MLE) of N. For the second scheme and a special case of the third, it is shown respectively that an MLE and an estimator which differs from an MLE by at most one have uniformly smaller mean square errors than the respective UMVUE's.
3
Content available remote

Unbiased estimation for two-parameter exponential distribution under time censored sampling

100%
Sengupta S.
Applicationes Mathematicae
|
2009
|
tom 36
|
nr 2
149-156
EN
The problem considered is that of unbiased estimation for a two-parameter exponential distribution under time censored sampling. We obtain a necessary form of an unbiasedly estimable parametric function and prove that there does not exist any unbiased estimator of the parameters and the mean of the distribution. For reliability estimation at a specified time point, we give a necessary and sufficient condition for the existence of an unbiased estimator and suggest an unbiased estimator based on a sufficient statistic in situations where unbiased estimators exist. Unbiased estimation of the variance of an unbiased estimator of reliability is also addressed.
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