Procedures for generating gamma variates with non-integer parameter sets

An approximate method for generating gamma and other variates

“…The percentiles for the gamma distribution were taken from Abramowitz and Stegun (1964). In addition to the approximation proposed here, approximations due to Phillips and Beightler (1972), Ramberg and Schmeiser (1974) and Ramberg and Tadikamalla (1973) are also given. The Ramberg and Tadikamalla (1974) algorithm is a modification of the Phillips and Beightler (1972) algorithm.…”

“…In addition to the approximation proposed here, approximations due to Phillips and Beightler (1972), Ramberg and Schmeiser (1974) and Ramberg and Tadikamalla (1973) are also given. The Ramberg and Tadikamalla (1974) algorithm is a modification of the Phillips and Beightler (1972) algorithm. The Ramberg and Schmeiser 1974) algorithm was given as a general approximation for asymmetric distributions.…”

“…(For example, see Phillips and Beightler (1972).) These equations need only be evaluated the first time a variate is generated for a given a.…”

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Phillips and Beightler (1972) gave an algorithm for generating gamma variates with noninteger parameter sets. The algorithm given here, which is based on a family of distribution~ developed by Burr (1942), is shown to be more accurate than that of Phillips and Beightler while the speed and memory requirements are comparable.

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Pitfalls with some gamma variate simulation routines

“…C~E S~& T P~ IXJ~:P-( 1 ) the algorithm byPhillips and Beightler (1972) 1 (2) the sum of exponentials rzutine; and (3) +&e rejechon I~chn~que of Johak (196A). For a!…”