Poisson distribution with parameter
Λ≥ 27, random numbers are generated by PTPE method (see [Schmeiser81] for details). Otherwise, a combination of inverse transformation and table lookup methods is used. The PTPE method is a variation of the acceptance/rejection method that uses linear (on the fraction close to the distribution mode) and exponential (at the distribution tails) functions as majorizing functions. To avoid time-consuming acceptance/rejection checks, areas with zero probability of rejection are introduced and a squeezing technique is applied.
See Intel® oneAPI Math Kernel Library Vector Statistics Random Number Generator Performance Data for test results summary and performance graphs.