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Level I

Creating Random distributions


For teaching purposes, I'm trying to create a dataset with 4 or 5 different distributions that all have a mean of 0 and sigma of 1. The lesson will be that sometimes the variation that is out there is more complicated than can be summarized from just those two numbers.

The first distribution is easy since it will be the "standard" normal distribution where the Random Normal() formula yields mean=0 and sigma=1, but then I get stuck because I haven't been able to figure out to adjust the skewness and kurtosis in the other random number sets. I would also like to add add a few other distribution types like exponential, geometric, and so on.

thanks for the help,
Super User ms
Super User

Re: Creating Random distributions

I think it will be difficult to achieve that if you restrict the the distribution parameters to mean=0 and sigma=1. Many distributions can't be defined by those parameters. For example, the exponential distribution postulate that mean = sigma (and mean always > 0).

But in principle you may use almost any of jmp's random generators to create random data from different distributions (or just use some real data) and then in other columns use the "col standardize" function to generate new data that by definition have mean =0 and sigma = 1. The standardized data can look skew and kurtotic but still have the properties of mean = 0 and sigma = 1.

But maybe you mean that you want to illustrate that samples taken from populations that follow specific distributions by chance may have a sample average of 0 and a sample standard deviation of one? That might involve a lot of trial and error. Or maybe I am totally missing the point here... (I am no probability expert).

Message was edited by: MS
Level I

Re: Creating Random distributions


I figured it out how to do it using the four-parameter Johnson distribution.

Good anticipation about using a mean of 0. I did change the mean to 10 so I could also use the exponential distribution.

- Sean
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