Uniformly Minimum-Variance Unbiased Estimator (UMVUE) for the Gamma Cumulative Distribution Function with Known and Integer Scale Parameter

作     者：Jessica Kubrusly Jessica Kubrusly

作者机构：Institute of Mathematics and Statistics Fluminense Federal University (UFF) Niterói Brazil 

出 版 物：《Open Journal of Statistics》 (统计学期刊（英文）)

年 卷 期：2022年第12卷第2期

页      面：168-174页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：UMVUE Cumulative Distribution Estimates Gamma Distribution Erlang Distribution Lehmann-Scheffeé Theorem Rao-Blackwell Theorem 

摘      要：Uniformly minimum-variance unbiased estimator (UMVUE) for the gamma cumulative 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.