Scaling Pareto between 1 and 0

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In summary, the conversation discusses creating a number generator using a pareto distribution. The problem is that the distribution goes from 0 to infinity, and the goal is to have a range between 0 and 1 instead. The method of generating generalized Pareto random variables from Wikipedia is being used, but the distribution doesn't start at 0 due to a singularity. The conversation then explores different options for scaling the values and finding a reasonable set of parameters for the desired distribution.
  • #1
jianxu
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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!
 
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  • #2
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.
 
  • #3
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!
 
  • #4
jianxu said:
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.
 
  • #5


Hello,

Thank you for sharing your project with me. It sounds like you are trying to scale the values of your Pareto distribution to fit within a range of 0 to 1. This is a common challenge in data analysis and there are a few ways to approach it.

One option is to use a transformation function, such as the inverse cumulative distribution function (CDF) of the Pareto distribution. This function can transform the values of your distribution to fit within a specific range, in this case 0 to 1. Alternatively, you could also use a rescaling method, where you multiply or divide your values by a constant factor to adjust the range.

It's important to note that scaling a distribution can affect its shape and statistical properties, so it's important to carefully consider the implications of your chosen method. I recommend consulting with a statistician or conducting some research on the specific effects of scaling a Pareto distribution before implementing your approach.

I hope this helps and good luck with your project!
 

1. What is Pareto scaling between 1 and 0?

Pareto scaling between 1 and 0 is a method used to transform data into a scale between 1 and 0, also known as a normalized scale. It is named after Vilfredo Pareto, an Italian economist, who first introduced the concept of a power law distribution.

2. How is Pareto scaling between 1 and 0 used in science?

In science, Pareto scaling between 1 and 0 is often used to normalize data that follows a power law distribution. This allows for easier comparison and analysis of different datasets, as it brings them to a common scale.

3. What are the benefits of using Pareto scaling between 1 and 0?

One of the main benefits of Pareto scaling between 1 and 0 is that it allows for easier comparison and analysis of data that follows a power law distribution. It also helps to reduce the influence of outliers and improve the interpretability of the data.

4. How is Pareto scaling between 1 and 0 different from other normalization methods?

Pareto scaling between 1 and 0 is different from other normalization methods, such as standardization or min-max scaling, as it specifically targets data that follows a power law distribution. Other methods may not be as effective in normalizing this type of data.

5. Can Pareto scaling between 1 and 0 be applied to all types of data?

Pareto scaling between 1 and 0 is most effective when applied to data that follows a power law distribution. However, it can be applied to other types of data as well, but the results may not be as significant or useful.

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