Distribution of xy/z. X,y,z ind uniform 0 to 1

[Nubyra]

Hi,

Can someone please help me solve the following:

Find the distribution of xy/z where x, y, z is independent and uniformly distributed from 0 to 1


Thanks for the help

 

[chiro]

Hi,

Can someone please help me solve the following:

Find the distribution of xy/z where x, y, z is independent and uniformly distributed from 0 to 1


Thanks for the help

Hey Nubyra and welcome to the forums.

Although I can't give you an analytic answer off the top of my head, one suggestion I do want to make is to use monte-carlo simulation to get a good idea of what the distribution should look like.

Most statistical problems will be able to simulate uniform by default so you should have no problems with this. I would recommend you use R since it is free, well documented, and is easy to use for this task.

http://www.r-project.org

 

[SW VandeCarr]

If you know the distribution functions you might be able to obtain the productf_1(x)f_2(y)f_3^{-1}( z) analytically.

http://en.wikipedia.org/wiki/Inverse_transform_sampling

http://mathworld.wolfram.com/UniformProductDistribution.html

http://mathworld.wolfram.com/InverseGaussianDistribution.html

http://mathworld.wolfram.com/NormalProductDistribution.html

EDIT: Most distributions can be restated in terms the Gaussian based on the sampling distribution and the Central Limit Theorem.