Random Variable Distributions

This page describes random distributions supported by Filebench

Uniform Distribution

DOMAIN: [a;b]

PDF: <math> f(x; a, b) = {1 \over {b - a}} </math>

CDF: <math> F(x; a, b) = {x - a \over {b - a}} </math>

EXPECTED: <math> (b - a) \over 2 </math>

DOMAIN: <math> [0:\infty) </math>

PDF: <math> f(x; \lambda) = \lambda e^{-\lambda x} </math>

CDF: <math> F(x; \lambda) = 1 - e^{-\lambda x} </math>

EXPECTED: <math> 1 \over \lambda </math>

DOMAIN: <math> [x:\infty) </math>

PDF: <math> f(x; k, \lambda) = {\lambda^{k} x^{k-1} e^{-\lambda x} \over \Gamma(k)} </math>

CDF: <math> F(x; k, \lambda) = {\gamma(k, \lambda x) \over \Gamma(k)} </math>

EXPECTED: <math> k \over \lambda </math>

In Erlang distribution k can be only integer. In Gamma distribution