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:

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).

Answer 3

Sounds like the Truncated Normal distribution is just what the doctor ordered. It is not "computationally simple" per se, but easy to implement if you have an existing implementation of a normal distribution.

You can just generate the distribution with the mean you want, standard deviation you want, and the two ends wherever you want. You'll have to do some work beforehand to compute the mean and standard deviation of the underlying (non-truncated) normal distribution to get the mean for the TN that you want, but you can use the formulae in that article. Also note that you can adjust the variance as well using this method :)

I have Java code (based on the Commons Math framework) for both an accurate (slower) and quick (less accurate) implementation of this distribution, with PDF, CDF, and sampling.