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randomprobabilitygaussianprobability-theory

Computationally simple pseudo-Gaussian distribution with varying mean and standard deviation?

This picture from Wikipedia has a nice example of the sort of functions I'd ideally like to generate:

pseudo-Gaussian distributions

Right now I'm using the Irwin-Hall Distribution, which is more or less a polynomial approximation of the Gaussian distribution...basically, you use uniform random number generator and iterate it x times, and take the average. The more iterations, the more like a Gaussian Distribution it is.

It's pretty nice; however I'd like to be able to have one where I can vary the mean. For example, let's say I wanted a number between the range 0 and 10, but around 7. Like, the mean (if I repeated this function multiple times) would turn out to be 7, but the actual range is 0-10.

Is there one I should look up, or should I work on doing some fancy maths with standard Gaussian distributions?

Solution

  • I see a contradiction in your question. From one side you want normal distribution which is symmetrical by it's nature, from other side you want the range asymmetrically disposed to mean value.

    I suspect you should try to look at other distributions density functions of which are like bell curve but asymmetrical. Like log distribution or beta distribution.