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Suppose that Y₁, Y2,..., Ym is a random sample of size m from Gamma(a = 3,ß = 0), where 0 is not known. Check whether or not the maximum likelihood estimator ê is a minimum variance unbiased estimator of the parameter 8.

Suppose that Y₁, Y2,..., Ym is a random sample of size m from Gamma(a = 3,ß = 0), where 0 is not known. Check whether or not the maximum likelihood estimator ê is a minimum variance unbiased estimator of the parameter 8.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Suppose that Y₁, Y2, ..., Ym is a random sample of size m from Gamma (a = 3,ß = 0), where 0 is not known. Check whether or not the maximum likelihood estimator ê is a minimum variance unbiased estimator of the parameter 0.
Transcribed Image Text:Suppose that Y₁, Y2, ..., Ym is a random sample of size m from Gamma (a = 3,ß = 0), where 0 is not known. Check whether or not the maximum likelihood estimator ê is a minimum variance unbiased estimator of the parameter 0.
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Step 1

Statistics homework question answer, step 1, image 1

Result: 

When score function S(x;θ) written in the form 

S(x; θ)=c(θ)[T-g(θ)] 

Then MLE attained CRLB and hence mle is the MVUE for parameter θ. 

 

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