Waiting-time distribution ($p(t)=-S^{\prime }(t)$)

The probability distribution of a nonnegative duration until an event. For a continuous duration with survival function $S(t)=P(T>t)$, its probability density function is $p(t)=-S^{\prime }(t)$. A constant hazard gives an exponential distribution; successive independent first-order waits give a convolution, as in the two-step catalytic waiting time.