Weibull Distribution |
(continuous probability dist for equations) |
Usage: |
WeibullDist (x, a, b) |
Definition: |
(a/b) (x/b)^(a-1) exp (-(x/b)^a) |
Parameters: |
a is shape b is scale |
Required: |
a > 0 b > 0 |
Support: |
x ³ 0 |
Moments: |
m = b gamma (1 + 1/a) s^2 = b^2 [gamma (1 + 2/a) - gamma (1 + 1/a) ^ 2] g1 = [gamma (1+3/a) - 3 gamma (1+1/a) gamma (1+2/a) + 2 gamma (1+1/a)^3] / [gamma (1+2/a) – gamma (1+1/a)^2]^(3/2) b2 = [gamma (1+4/a) - 4 gamma (1+1/a) gamma (1+3/a) + 6 gamma (1+1/a)^2 gamma (1+2/a) - 3 gamma (1+1/a)^4] / [gamma (1+2/a) - gamma (1+1/a)^2]^2 |
The Weibull distribution is often used for reliability models, since if the failure rate of an item (i.e., percent of the remaining ones which fail, as a function of time) is given as: Z(t) = r t^(a-1), then the distribution of item lifetimes is given by the Weibull distribution with r = a / b ^ a.