Statistical Sciences 2141A/B Lecture 23: Section 7.4

• School: Western University
• Department: Statistical Sciences
• Course: Statistical Sciences 2141A/B
• Professor: Joe Raaymakers

Document Summary

Let"s equate certain sample characteristics, such as the mean, to the corresponding population expected values and solve these equations for the unknown parameter values. Let x1 , x2 , , xn (cid:271)e a se(cid:395)uen(cid:272)e of iid (cid:396)(cid:448)"s. Fo(cid:396) k =(cid:1005), (cid:1006), (cid:1007), , the kth population moment (or kth moment of the distribution) is e(k). The kth sample moment is (cid:1005) (cid:1006) (cid:1005) (cid:1006) Particularly: (cid:1005) (cid:1006) n (cid:1005) (cid:1006) n (cid:1005) (cid:1006) (cid:1005) (cid:1006) Let x1 , x2 , , xn (cid:271)e a se(cid:395)uen(cid:272)e of iid (cid:396)(cid:448)"s (cid:449)ith the p(cid:396)o(cid:271)a(cid:271)ilit(cid:455) dist(cid:396)i(cid:271)ution (cid:894)i. e. , p f o(cid:396) pdf(cid:895) f(cid:894)(cid:454); (cid:1005) , , m) depending on 1 , , m. T (cid:1005) (cid:1006) (cid:1005) (cid:1006) ( ; ) = ( 1 ; ( ; ) In practice, the maximization of the likelihood function is usually performed by taking the partial derivative with respect to each parameter value.