ABSTRACT
The probability density function of the extreme value distribution with the location parameter a and the scale parameter b is given by
f(x|a, b) = 1 b exp[−(x− a)/b] exp{− exp[−(x− a)/b]}, b > 0. (25.1.1)
The cumulative distribution function is given by
F (x|a, b) = exp{− exp[−(x− a)/b]}, −∞ < x <∞, b > 0. (25.1.2)
The inverse distribution function is given by
F−1(p|a, b) = a− b ln(− ln(p)), 0 < p < 1. (25.1.3)
We refer to this distribution as extreme(a, b). The family of distributions of the form (25.1.2) is referred to as Type I family. Other families of extreme value distributions are:
Type II:
F (x|a, b) = {
0 for x < a, exp{− (x−ab )−k} for x ≥ a, k > 0.
