Question

1. Assume n i.id. draws from Y ~ Weibull(9,%), with pdf: where γ-γ0 is a given value and the only unknown parameter is θ. (a) Show that the distribution of Y (for given γ-γ°) admits MyBU estimation of a particular function ψ(0) by showing that the joint pdf. f(y|θ, γ0), belongs to the exponential family with: TL K (e) TL (b) It can be shown that the median of Y is median(Yja, γο-θ(log 2) 1/γο, Take as a given (i.e. you do not have to work it out!), where: 82 and _ (Y, Y, , Yn). Defining ψ(9) as the function of θ given in (1) (for fixed γ-γ ), give the Cramer Rao lower bound for the variance of all unbiased estimators of ψ(0) (c) Using the relevant results in Q1(a) above and the expression for the median of Y in (1), demonstrate that the Weibull distribution (with fixed γ %) does not admit MVBU estimation of the median of Y (for arbitrary yo). Is there a particular value of "Yo for which MVBU estimation of the median of Y is feasible?

Answer 1