SHARP TWO-SIDED BOUNDS FOR DISTRIBUTIONS UNDER A HAZARD RATE CONSTRAINT

Consider a continuous nonnegative random variable X with mean μ and hazard function h. Assume further that a ≤ h(t) ≤ b for all t ≥ 0. Under these constraints, we obtain sharp two-sided bounds for .F(t) = Pr(X > t). An application to birth and death processes is discussed.