(a) Let T 1 ,…,T n be a random sample from a distribution with survivor function F(t) and…

(a) Let T1,…,Tn be a random sample from a distribution with survivor function F(t) and suppose that as t →  0,

for some λ > 0. Show that the limiting distribution of Xn = η min (T1,…,T2) is exponential with failure rate λ. As noted in Section 2.2.1, this property is sometimes taken as justification for the choice of an exponential model

(b) Suppose now that for t near 0,

is Weibull with shape Y and scale λ.