Weibull Distribution

Let Y be a standard exponential random variable with probability density function

f(y) = e−y, y > 0.

Define X = bY 1/c +m, b > 0, c > 0.

The distribution ofX is known as the Weibull distribution with shape parameter c, scale parameter b, and the location parameter m. Its probability density is given by

f(x|b, c,m) = c b

( x−m b

{ − [ x−m b

]c} , x > m, b > 0, c > 0.