Using the results of
3.1, determine the expected information matrix for the Weibull distribution with density function
Exercise
(a) Use expression (3.4) to show that if tn) is the largest of η independent unit exponential variates, the rth cumulant of I t(n )is
(b) Show that the asymptotic distribution of is the extreme value distribution with density (2.1). Note also that the MGF of X„ converges uniformly for , 1) to the MGF of (2.1). This implies
(c) By making use of parts (a) and (b), show that the extreme value density has cumulants