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Uniformly Minimum-Variance Unbiased Estimator (UMVUE) for the Gamma Cumulative Distribution Function with Known and Integer Scale Parameter
Institute of Mathematics and Statistics, Fluminense Federal University (UFF), Niterói, Brazil
- 1 Institute of Mathematics and Statistics, Fluminense Federal University (UFF), Niterói, Brazil
Open Journal of Statistics·Volume 12 (2022)·Pages 168–174·Published 14 March 2022·DOI10.4236/ojs.2022.122011
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Abstract
Uniformly minimum-variance unbiased estimator (UMVUE) for the gamma c umulative distribution function with known and integer scale parameter. This paper applies Rao-Blackwell and Lehmann-Scheffeé Theorems to deduce the uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative distribution function with known and integer scale parameters. The paper closes with an example comparing the empirical distribution function with the UMVUE estimates.
KeywordsUMVUECumulative Distribution EstimatesGamma DistributionErlang DistributionLehmann-ScheffeéTheoremRao-Blackwell Theorem
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