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I am curious about some glossaries.

  1. Does "pseudorandom number generator (PRNG)" only mean for uniform random number generator? I didn't see one that is not in list of random number generators.

  2. Does "Pseudo-random number sampling" only mean for non-uniform random number generator?

    Pseudo-random number sampling or non-uniform pseudo-random variate generation is the numerical practice of generating pseudo-random numbers that are distributed according to a given probability distribution.

Thanks!

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RNGs, be it pseudo or quasi, are most often constructed for the Uniform distribution. They can then used for a given distribution via inversion, or better methods.

The Normal distribution is an exception as it is so frequently used, and special algorithm exists (with Box-Muller being a well-known one).

Most statistical computing texts cover this in some detail.

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  • $\begingroup$ @MichaelChernick: Thanks -- I was actually in a rush to get out the door for work and couldn't fill in more references. Maybe this eve :) $\endgroup$
    – Dirk Eddelbuettel
    Commented Sep 24, 2012 at 13:05
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    $\begingroup$ As I understand it, the Box-Muller method also uses uniform random number generators (in fact, two successive outputs from a PRNG) to create two independent samples from a (standard) normal distribution. $\endgroup$
    – Dilip Sarwate
    Commented Sep 24, 2012 at 15:12
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    $\begingroup$ Thanks! What references were you planning to fill in? $\endgroup$
    – Tim
    Commented Sep 29, 2012 at 3:40
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    $\begingroup$ Well, I have Eubank and Kupresian, "Statistical Computing in C++ and R", 2011, CRC Press on my desk right now which definitely covers this, but so do a few other books as eg the books by Gentle should have something on this, as should the older Statistical Simulation (?) book by Ripley. $\endgroup$
    – Dirk Eddelbuettel
    Commented Sep 29, 2012 at 3:44

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