Exponential Distribution (Survival)

Definition

Exponential Distribution for survival: Simplest model; assumes constant hazard rate. Has “lack of memory” property.

For $T\sim \text{Exp}(\lambda )$, $\lambda >0$:

$$\begin{array}{rl}f(t)& =\lambda e^{-\lambda t},t>0\\ S(t)& =e^{-\lambda t}\\ h(t)& =\lambda \\ H(t)& =\lambda t\\ E(T)& =\frac{1}{\lambda },V(T)=\frac{1}{{\lambda }^2}\end{array}$$

Property: Constant Hazard

Notice that $h(t)=\lambda$ is constant. We can interpret $\lambda$ as the hazard rate—see hazard function interpretation.

Related

• Weibull Distribution (Survival)
• Parametric Survival Distributions Cheatsheet