Uniform frailty survival mixture ($\overline{S}(t)=\frac{e^{-a\theta t}-e^{-b\theta t}}{(b-a)\theta t}$)

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 isIt 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.