I am an BSc(Hon)Applied Mathematics Graduate from University of South Africa
Operations Research "Simulation" I am very familiar with it.
This is a simple problem for me but I have given a details in a nut-shell in terms of how I can do it
Simulation for Normal distribution (as an example)
Generate U1, U2, …, Un ~ U(0; 1)
Return X ( I can't write relevant formula here)
We can do a test if necessary:
The chi-square goodness-of-fit test can be applied to check whether the sequence of random numbers
appear to be uniformly distributed between 0 and 1. It is a special case of the chi-square test with all
parameters known. We divide the interval [0; 1] into k intervals of equal length and generate n
random numbers, U1, U2, …, Un . As a general rule n should be at least 100 here and n/k should be at least 5
Or we can use Kolmogorov-Smirnov test for goodness of fit.
A matrix with 100 rows and 2 columns can be presented on a spread sheet where all the necessary calculations and abovementioned test for consistence of our random generation U1,U2,..Un;
n(0,100) will be done.
Further calculations will be to generate z-vectors (n-independent) using Box-Muller Transformer.
And then use z to determine x = μ + A*z
You can call me +2761 031 0619 I am based in south Africa