I want to generate data for vector 'y' between 'x_min' and 'x_max'. The data need to be generated to be in such a way that they would return certain 'mu' and 'sigma' if I fit them for normal distribution. Can you advise please?
You won't be able to accomplish this for general x_min, x_max, mu, and sigma. The reason is that the probability density function of a normal distribution is nonzero over the open interval (-inf,inf).
However, you can do reasonably well if, for example, x_min - 3*sigma < mu < x_max + 3*sigma. Then, when you randomly generate data in accordance with a normal distribution, pretty much all of the data you generate will lie between x_min and x_max. Just throw out those that don't.
In MATLAB, for a sample of approximate size n (it may end up being a little less), you can do it in three lines of code.
y = sigma*randn(n,1) + mu; % Data from N(mu,sigma^2)
m = find((y >= x_min) & (y
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Why are you trying to coerce a normal distribution into a defined range? What are you trying to simulate? There may be better ways of generating data that more closely mirror the data generation process you are interested in.
Dear Al-Motasem I Aldaoudeyeh,
You can use the acceptance-rejection method to generate random numbers that satisfy certain 'mu' and 'sigma' for normal distribution f(x). The algorithm to obtain a sample from distribution with normal density f(x) is as follows:
1.Generate a value of a random variable Xi with uniform distribution from (x_min, x_max).
2.Generate a value of a random variable Yi with uniform distribution from (0, f_max).
3.If Yi
You can do it easily using Mathematica. There is a command that helps you generate random data from any prescribed distribution.
The following command generates 10 random observations x from the normal distribution with mean 5 and standard deviation 3 such that -1
The Box-Muller method is the most used for generating random normal distributed numbers. It’s very easy to implement and you can used in any language that has a built-in uniform number generator.
Good Luck!
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