MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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4. Given a gamma distribution with alpha equal to 3 and B unknown. Find the
Cramer Rao Lower Bound for the variance of all unbiased estimators of ß.
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Transcribed Image Text:4. Given a gamma distribution with alpha equal to 3 and B unknown. Find the Cramer Rao Lower Bound for the variance of all unbiased estimators of ß.
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4.

From the given information, the gamma distribution with alpha equal to 3 and β unknown.

Let us consider X1,X2,.....,Xn be the random sample follows γα=3, β

The probability density function for Xi is,

f(x)=βαγαxα-1e-βx      =β3γ3x3-1e-βx      =β32x2e-βx

Unbiased estimator for β:

Mean=Xin     αβ=Xin     3β=Xin      β^=3nXi

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