Notes for Intel® oneAPI Math Kernel Library Vector Statistics

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Multinomial (VSL_RNG_METHOD_MULTINOMIAL_MULTPOISSON)

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
    (X
    1
    ...X
    k
    )
     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
        U
        i
         are generated on the interval (0, 1).
      2. The component
        X
        i
         is incremented by 1 if

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