ABSTRACT
In Chapter 2, we have seen the basic properties of a Weibull distribution. A random variable X is said to have a (two-parameter) Weibull distribution, or Weibull(α, β), with parameters α and β provided the pdf of X is given as
f(x ∣∣α, β) = α
βα xα−1e−(x/β)
, 0 < x <∞, α > 0, β > 0 (8.1.1)
When β = 1, the pdf (8.1.1) is reduced to
f(x ∣∣α, 1) = αxα−1e−xα , x > 0, α > 0 (8.1.2)
and this is known as the Standard Weibull distribution. The distribution is named after Waloddi Weibull, a Swedish physi-
cist, who used it to represent the probability distribution of the breaking strength of materials. The use of the Weibull distribution in reliability and quality control work has been advocated by Kao (1958, 1959).
