A computationally simple pseudo-Gaussian distribution with a variable mean and standard deviation?

Question

This Wikipedia photo has a nice example of what features I would like to create:

Now I use the Irwin-Hall Distribution distribution, which is more or less polynomial approximation of the Gaussian distribution ... basically, you use the random number generator and repeat it x times and take the average value. The more iterations, the more like the Gaussian distribution.

This is pretty good; however, I would like to have one where I can change the average value. For example, suppose I need a number between the range 0 and 10, but about 7. For example, the average value (if I repeat this function several times) is 7, but the actual range is 0-10.

Is there one of them that I should look for, or should I work on some fantastic mathematicians with standard Gaussian distributions?

Answer 1

I see a contradiction in your question. On the one hand, you want a normal distribution that is symmetrical in nature, on the other hand, you want the range asymmetrically to be in the middle value.

I suspect you should try to look at other density distribution functions, which, like bell curves, are asymmetrical. Like magazine distribution or beta .

Answer 2

Look at the generation of ordinary random variations . You can generate pairs of normal random variations X = N (0,1) and convert them to ANY ordinary random fluctuations Y = N (m, s) (Y = m + s * X).

Answer 3

Truncated Normal appears to be what the doctor ordered. It is not “computationally simple” as such, but easy to implement if you have an existing implementation of the normal distribution.

You can simply create a distribution with the average you want, the standard deviation you want, and the two ends where you want. You will need to do some work in advance to calculate the mean and standard deviation of the base (not truncated) normal distribution to get the mean value for TN that you want, but you can use the formulas in this article. Also note that you can also adjust the variance using this method :)

I have Java code (based on the Commons Math framework) for the exact (slow) and fast (less accurate) version of this distribution using PDF, CDF and fetch.