Let T > 0 be a continuous random variable with cumulative hazard function H(·). Show that...

Let T > 0 be a continuous random variable with cumulative hazard function H(·).

Show that H(T)∼Exp(1),where Exp(λ) in general denotes the exponential distribution with rate parameter λ.

Hints:

(a) You can use the following fact without proof: For any continuous random variable T with cumulative distribution function F(·), F(T) ∼ Unif(0,1). Hence S(T) ∼ Unif(0,1).

(b) Use the relationship between S(t) and H(t) to derive that Pr(H(T) > x)= e−x.

Expert Solution

orchestra answered 2 years ago

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