Notes for Intel® oneAPI Math Kernel Library Vector Statistics

ID 772987
Date 12/04/2020
Document Table of Contents


Multinomial distribution with parameters m, k, and a probability vector p. Random numbers of the multinomial distribution are generated by Poisson Approximation method (see [Charles93] for details).

  1. In the first stage, k independent Poisson values (X1...Xk) are generated by the POISSNORM method.
  2. Let m* denote sum of the generated k Poisson variates:
    • If m*=m, the first-stage sample has the required distribution.
    • If m*>m, the sample is discarded and the first stage is repeated.
    • If m*<m, m*-m observations are generated by the Direct method (see [Charles93] for details):
      1. m*-m uniformly distributed independent random variates Ui are generated on the interval (0, 1).
      2. The component Xi is incremented by 1 if

See Intel® oneAPI Math Kernel Library Vector Statistics Random Number Generator Performance Data for test results summary and performance graphs.