Consider a survival time T with survival function S(t) and cumulative distribution function   and assume that the cumulative distribution function is continuous and strictly increasing. Then the pth...

Consider a survival time T with survival function S(t) and cumulative distribution function
  and assume that the cumulative distribution function is continuous and strictly increasing. Then the pth fractile ξp of the distribution is uniquely determined by the relation
 Of particular interest are the median ξ0.50 and the lower and upper quartiles

a) Show that ξ_p
is uniquely determined by the relation A
  where A(t) is the cumulative hazard rate (1.3).

b) Find expressions for
 for the exponential distribution and the Weibull distribution (cf. Exercise 1.1).