Exact Sequential Simulation of Binary Varibles Given Their Sum
Arne Bang Huseby · NORA - Norwegian Open Research Archives · 2004
The paper considers the problem of simulating a vector, Xof n independent binary variables conditioned on their sum, S. For a fixed value of S an exact simulation method is provided in Huseby and Naustdal [4].In certain situations, however, it is of interest to generate an increasing sequence of binary vectors X1 < • • • < Xn, such that the s-th vector is distributed as the vector Xgiven S = s, s = 1, . . ., n.If all the variables of the vector Xare identically distributed, it can be shown that this is equivalent to generating a random permutation, {πs} n s=1 , of the index set, {1, . . ., n}.For more details about this, see Huseby and Naustdal[4].In the present paper, however, we provide a simulation algorithm for the case when the variables of the vector Xdo not necessarily have the same distribution.This algorithm utilizes the fact that the distribution of a sum of independent binary variables is always log-concave.