Generate Probability Denisity function from a uniform one

[frigi64]

Hello,
I was wondering if anyone knew (or could direct me) of how to generate any probability density function from from a uniform distribution. For example from uniform to Rayleigh (or exponential).

I am interested both in the mathematical derivation and the software implementation (Matlab).

Thanks.

 

[dspman]

Hi,

It is very simple!!
You have pass the uniform data (between 0 and one) through the inverse cdf (cumulative distribution function) of the required Distribution. ie if you want to generate a distribution with cdf as 1-exp(-x) for x>0 you have to use -ln(1-x).
the code is also simple:

X=rand(1,1e4);
Y=-log(1-X);
hist(Y,50)

Hope it helped.
dspman

 

[frigi64]

Re: Generate Probability Denisity function from a uniform o

Hello,

Thanks for your response.
I am confused as to why you are using -In(1-x);

According to https://en.wikipedia.org/wiki/Exponential_distribution
the inverse cdf of the exponential is:

1 - exp(-lambda*x);

From your explanation:
You have pass the uniform data (between 0 and one) through the inverse cdf (cumulative distribution function) of the required Distribution.

Working from there I thought that this is what the code should look like:

X=rand(1,1e4);
Y = 1 - exp(-lambda*X);

Where X is the original uniformly distributed data and Y is the exponentially distributed data.

Please let me know if that is correct or if I completely missed the gist of what you were saying.

Thanks.

 

[dspman]

In order to find the inverse cdf of the exponential distribution I have solved Y=1-exp(-X) for X. This is the point. You have to find algebric inverse.
Also if you jenerate the data using the line you have here, I think you can see that the drived data are not exponentially distributed.

Yours,
dspman.

 

[farhadtehrani]

Re: Generate Probability Denisity function from a uniform o

this is unavaibale problem???!!!

 

[Sal]

HI

here is the Gaussian case

https://www.taygeta.com/random/gaussian.html

Sal

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