The weibull distribution as mixture of exponential distributions

الملخص EN

The Weibull distribution is named after the physicist W.

Weibull who used it in 1939 as the distribution of the fatigue and breaking strength of materials.

It is also used as a failure time distribution.

In this paper, we show how it is possible to approximate a Weibull distribution arbitrarily closely by finite mixtures of exponential distributions.

A continuous random variable U is defined to have a finite mixture of exponential distributions with parameters Pi > 0 for i = 1,2, ...,r and £[=iPi = 1, if its cumulative distribution function (cdf) has the form Hr(u, = 1 — ^[=1 pte-XiU where ^ = (p1, ,.,pr,A1, ...,Ar).

Two algorithms for approximating finite mixtures of exponential distributions, with an explanation of when these algorithms should be effective, are also considered in this paper.