00900 Gamma Distribution Exercise. To determine the variance of these estimators, compute the app...
00900 Gamma Distribution Exercise. To determine the variance of these estimators, compute the appropriate second derivatives. o? a2 θα β This give a Fisher information matrix /(α, β)::n( ) Inf(a) In r(a) - -a 1(0.19, 5.18) (0.19,5.18) 500 28.983 -0.193 500 NB. ψι(a) d2mT(a)/da2 is known as the trigamma function and is called in R with trigamma. 8/10 00090 Gamma Distribution The inverse matrix 1 0.0422 1.1494 /(α, β)--500 (1.1494 172.5587 Var(a) ~ 8.432 x 10-5 σ& 0.00918 Var(8) 0.3451...
Exercise: Let Yİ,Y2, ,, be a random sample from a Gamma distribution with parameters and β. Assume α > 0 is known. a. Find the Maximum Likelihood Estimator for β. b. Show that the MLE is consistent for β. c. Find a sufficient statistic for β. d. Find a minimum variance unbiased estimator of β. e. Find a uniformly most powerful test for HO : β-2 vs. HA : β > 2. (Assume P(Type!Error)- 0.05, n 10 and a -...