STAT231 Study Guide - Quiz Guide: Maximum Likelihood Estimation, Likelihood Function

• School: University of Waterloo
• Department: Statistics
• Course: STAT231
• Professor: Matthias Schonlau

Document Summary

X= # of trials before the first success in a bernoulli experiment. P(x = 3) = (1 )2 and so on. In general, the distribution function is given by f (n) = p(x = n) = (1 )n 1 , n =1,2,: the likelihood function is given by. = n(1 ) (xi 1) n i =1 i. e. the simplified likelihood function is given by. L( ) = n(1 ) xi n: the log-likelihood function is given by l( ) = lnl( ) R( ) = nln +( nln xi n)ln(1 ) xi n)ln(1 where pi(hat) is the mle calculated in ( c) To calculate the mle, we take derivative of the log-likelihood function and equate it to zero dl d i. e. n. Solving the above equation, we get the mle xi n . The proof is best illustrated with an example for a more formal proof, see the following link: http://ocw. mit. edu/courses/mathematics/18-443-statistics-for-applications-fall-2006/lecture- notes/lecture2. pdf (page 13)