Computationally simple Pseudo-Gaussian Distribution with varying mean and standard deviation?

Question

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

http://en.wikipedia.org/wiki/File:Normal_Distribution_PDF.svg

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?

Answer 1

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.

Answer 2

Look into generating normal random variates. You can generate pairs of normal random variates X = N(0,1) and tranform it into ANY normal random variate Y = N(m,s) (Y = m + s*X).