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Having a dataset and calculating statistics from it is easy. How about the other way around?
Let’s say I know some variable has an average X, standard deviation Y and assume it has normal (Gaussian) distribution. What would be the best way to generate a “random” dataset (of arbitrary size) which will fit the distribution?
EDIT: This kind of develops from this question; I could make something based on that method, but I am wondering if there’s a more efficient way to do it.
You can generate standard normal random variables with the Box-Mueller method. Then to transform that to have mean mu and standard deviation sigma, multiply your samples by sigma and add mu. I.e. for each z from the standard normal, return mu + sigma*z.