= Uniform frailty survival mixture
{title2=$\overline S(t)=\frac{e^{-a\theta t}-e^{-b\theta t}}{(b-a)\theta t}$}
Let the <frailty random variable> be uniform on $[a,b]$ with $0<a<b$, and let the conditional individual <hazard function> be the constant $U\theta$, $\theta>0$. Averaging conditional exponential survivor functions gives the displayed population <survivor function> for $t>0$, with value one at zero. Its <population hazard of a survival mixture> is
$$
\overline h(t)=a\theta+\frac1t-\frac{(b-a)\theta}{e^{(b-a)\theta t}-1}.
$$
It starts at $\theta(a+b)/2$ and tends to $a\theta$: the <frailty distribution among survivors> progressively concentrates near its smallest frailty. Although each individual's hazard is constant, the population hazard decreases through survival selection.
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