What algorithm does random(makedist) use

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I have a pdf similar to the generalized normal distribution function, but it has an additional complication so that it includes the family of skewed distributions also. I can easily sample from the generalized normal distribution using an appropriate transformation. I don't know how to convert the samples from the generalized normal distribution to the required distribution using simple transformations. I want to avoid using the algorithms such as Accept-Reject or Metropolis-Hasting. I see that MatLab function 'makedist' with 'random' samples from custom distributions. I need to know which algorithm does it use to do so?

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