Cumulative distribution function of a function of a random variable

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Hi everyone
I have the following issue:
X is a random variable uniform between
The variable Y is a function of X:
where α is a constant.
I can't solve the equation for X, so I can't find the cumulative distribution of Y analytically. Is there a possibility in Matlab to find the cdf of a function of a Random Variable with a known cdf?
Thanks for your help!

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Accepted Answer

David Goodmanson
David Goodmanson on 15 Aug 2019
Hi Franziska,
a = 1.2;
x = .2
y = a*(1+x)*(2/(1+ (1+x)^(1/(a-1))))^(a-1)
xx = (y/a)/(2-(y/a)^(1/(a-1)))^(a-1) -1 % inverse function f(y)
x = 0.2000
y = 1.2884
xx = 0.2000 % same
try some values ,,,
Franziska on 16 Aug 2019
Fantastic! Thanks for explaining the steps, that was very helpful.

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