How to Scale a Pareto Distribution Between 0 and 1?

[jianxu]

Hello and thank you for taking the time to read this.

I am making a number generator that generates a number based on a pareto distribution.
The problem is, the distribution essentially goes from 0 to infinity. How would I go about scaling the values so I get a range between 0 and 1 instead?

As of right now, I'm taking a random uniform number and simply turning it into a pareto distribution using a method called Generating generalized Pareto random variables (found in wikipedia).

Thanks again!

 

[sfs01]

I think you need to specify more exactly what kind of probability distribution you want. The Pareto distribution doesn't start at zero because the PDF has a singularity there, so it can't integrate to 1.

Do you want the whole Pareto range rescaled onto the interval from 0 to 1? If you do that, it won't be a Pareto distribution anymore by any stretch of the imagination.

Or do you want a Pareto-like power law distribution that goes from 0 to 1? Once you have decided which pdf you want (e.g.
a bounded Pareto distribution shifted/scaled to start at zero), that should be fairly straightforward, you should be able to calculate the CDF and invert it - which you can use to transform a uniform variable into your distribution.

 

[jianxu]

Hello,

Thanks for the reply and sorry for the confusion.
I think a pareto like distribution from 0 to 1 is what I'm going for.
So would I just have it be bounded between 0 and 1?
Thanks!

 

[sfs01]

Hello,

Thanks for the reply and sorry for the confusion.
I think a pareto like distribution from 0 to 1 is what I'm going for.
So would I just have it be bounded between 0 and 1?
Thanks!

In that case the bounded Pareto distribution (also described on the wikipedia page) is probably what you are looking for. That is only defined for ranges that start at values greater than zero though, so you'll have to pick some range and then linearly scale/shift the values to your desired range. Which range you pick for the original bounded Pareto distribution will have quite a significant effect on the shape of the resulting distribution, so you'll need to find a reasonable set of parameters for whatever you're modelling.