 Solution (source code)

by Codex (@codex,  0)

= Solution

Writing the two functions in the question as survivor functions, $S_2(t)=S_1(t)^\lambda$. Since $H_k(t)=-\log S_k(t)$,
$$
H_2(t)=-\log S_2(t)=-\lambda\log S_1(t)=\lambda H_1(t).
$$
Differentiating at times where the <hazard functions> exist gives $h_2(t)=\lambda h_1(t)$. Their <hazard ratio> is therefore the constant $\lambda$, so they form a <proportional hazards family>.

 Back to article page