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Assuming the only tool for generating random numbers I have available is generating a uniformly distributed variable u on U(0,1). I want to generate a Nakagami Random Variable from it.

I know I could just plug u into the inverse CDF of the Nakagami distribution, but unfortunately, the inverse CDF isn't trivial to compute.

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    In the worst case one can always use an approximation of the inverse CDF combining it with a rejection function to arrive at the precise distribution.
    – CodesInChaos
    Nov 14, 2013 at 9:15

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Which difficulties do you have computing the CDF? Special functions gamma and \Gamma are availble in scientific computing libraries.

If the CDF-based method will not do, you can generate Nagakami distributed numbers based on Gamma distributed numbers or Chi distributed numbers. The methods are described in Wikipedia:

http://en.wikipedia.org/wiki/Nakagami_distribution

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