Why is the Exponential Distribution special?

1. Beta = 1
2. Constant failure rate (or, hazard rate = lambda) -> used to model useful life portion of the bathtub curve.
3. R(t+T) = R(t)
4. A 3-parameter Weibull(eta, beta, gamma) is the same as a 2-parameter exponential (with beta = 1 & eta = MTTF = 1/lambda).
5. A 1-parameter Weibull (eta, beta=1, gamma=0) is the same as 1-parameter exponential (with eta = MTTF = 1/lambda)
6. R(t=MTTF) = 36.8% & Q(t=MTTF) = 63.2%.