Consider the comparison of two type II censored samples where sample / is followed to the…

Consider the comparison of two type II censored samples where sample / is followed to the observed djth failure,  — 1,2.

(a) In the notation of Section 3.3, show that  has an F distribution on 2di and 2d2 degrees of freedom.

(b) Suppose that d1 = 17 and d2 = 19 and it is observed that V1=219 5 and V2 = 2923. Compute a 95% confidence interval for  compare with the results given in Section 3.5.2 for the same data but with type I censoring.

(c) For large degrees of freedom, the logarithm of an F( n m ) variate is approximately normal with mean (Atiquallah, 1962). Use this result to obtain an approximate normal distribution for   and compare it with the asymptotic normal distribution of in Section 3.5.2.