Weibull distribution
Definition taught in Reliability, part of Probability
Weibull distribution
| Type | Definition |
| Taught in | Reliability |
| Part | Probability |
A lifetime T is Weibull with shape \beta>0 and rate \lambda>0 when its density is \lambda\beta\,(\lambda t)^{\beta-1}\exp(-(\lambda t)^\beta) for t>0. The survival function is \exp(-(\lambda t)^\beta), the distribution function is 1 minus that survival function, and
\mathbb{E} T=\frac{\Gamma(1+1/\beta)}{\lambda}.
The shape \beta=1 is the exponential distribution with rate \lambda.
Used in
- Taught in Reliability, where the derivation and examples are.
- All 7 questions on Reliability
See also
Survival function · Cumulative distribution function · Exponential distribution · Structure function · Reliability function · Hazard rate