ABSTRACT
A random variable X is said to have a Type-I Extreme Value (EV) distribution with parameters μ and β provided the pdf of X is given as
f1(x | μ, β) = 1 β e−(x−μ)/β exp
{ −e−(x−μ)/β
} , x ∈ , β > 0, μ ∈ (9.1.1)
The above positively skewed pdf with range over the whole real line has the cdf
F1(x) = P (X ≤ x) = exp { −e−(x−μ)/β
} (9.1.2)
and henceforth the distribution will be called as EV-I(β, μ) distribution. When β = 1 and μ = 0, the above pdf (9.1.1) reduces to
f1(x | 0, 1) = e−xexp {−e−x} (9.1.3)
and this is known as EV-I(1, 0) or standard Type I Extreme Value Distribution.
