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Chapter 10: Q. 10.5 (page 431)

Use the inverse transformation method to present an approach for generating a random variable from the Weibull distribution

F(t)=1-e-at尾t鈮�0

Short Answer

Expert verified

The required method is used for the solution and it is explained below.

Step by step solution

01

Given Information

We have given Weibull distribution

F(t)=1-e-at尾t鈮�0

02

Simplify

FindingF-1. forlocalid="1648201218153" y鈭�(0,1)we have

F(t)=1-e-at尾=y

1-y=e-at尾

log(1-y)=-at尾

-1alog(1-y)=t尾

localid="1648201140915" t=-1alog(1-y)1尾

So, the method is as follows. choose a random number (call it y) from the interval (0,1)and declare that localid="1651486180967" t=-1alog(1-y)1尾. from the universality of the uniform, we have that xfollows the distribution of X

log(1-y)=-at尾

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