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(i) | if , Johnk's algorithm is used, see for example Dagpunar (1988). This generates the beta variate as , where and are uniformly distributed random variates; |
(ii) | if , the algorithm BB given by Cheng (1978) is used. This involves the generation of an observation from a beta distribution of the second kind by the envelope rejection method using a log-logistic target distribution and then transforming it to a beta variate; |
(iii) | if and , the switching algorithm given by Atkinson (1979) is used. The two target distributions used are and , along with the approximation to the switching parameter of ; |
(iv) | in all other cases, Cheng's BC algorithm (see Cheng (1978)) is used with modifications suggested by Dagpunar (1988). This algorithm is similar to BB, used when , but is tuned for small values of and . |
On entry, | STATE vector was not initialized or has been corrupted. |