ABSTRACT
The probability density function of a Pareto distribution with parameters a and b is given by
f(x|a, b) = ba b
xb+1 , x ≥ a > 0, b > 0. (23.1.1)
The cumulative distribution function is given by
F (x|a, b) = P (X ≤ x|a, b) = 1− ( a
x
)b , x ≥ a. (23.1.2)
For any given 0 < p < 1, the inverse distribution function is
F−1(p|a, b) = a (1− p)1/b . (23.1.3)
Plots of the pdfs are given in Figure 23.1 for b = 1, 2, 3 and a = 1. All the plots show long right tail; this distribution may be postulated if the data exhibit a long right tail.
