20
2. Cumulative distribution function (cdf),
t
F(t) = P[T<t∖ = I f(s)ds. (2.6)
о
A cumulative distribution function is a cumulative function of pdf.
3. Survival function,
∞
S(t) = P[T>t] = l- F(t) = J f(s)ds. (2.7)
t
A survival function S(t) indicates the probability that a person survives longer
than some specified time t. The range of a survival function is from 0 to 1. A survival
function is a monotone function by time.
4. Hazard function,
X(fj = Hm ɪp [t < T < t + Δi∣T > t] = ⅛4.
(2-8)
' , Δt→o∆f l - - ∣-J
A hazard function or hazard rate indicates instantaneous death rate at time t,
given alive up to t.
5. Cumulative hazard function,
t
Λ(i) = ʃ λ(s)ds = —Zn(S(f)).
о
(2.9)
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