randomTableTwoway¶

Generates a pseudorandom two-way table.

Synopsis¶

randomTableTwoway (nrtot, nctot)

Required Arguments¶

int nrtot[] (Input): Array of length nrow containing the row totals.
int nctot[] (Input): Array of length ncol containing the column totals. The elements of nrtot and nctot must be nonnegative and must sum to the same quantity.

Return Value¶

nrow by ncol random matrix with the given row and column totals.

Description¶

Function randomTableTwoway generates pseudorandom entries for a two-way contingency table with fixed row and column totals. The method depends on the size of the table and the total number of entries in the table. If the total number of entries is less than twice the product of the number of rows and columns, the method described by Boyette (1979) and by Agresti, Wackerly, and Boyette (1979) is used. In this method, a work vector is filled with row indices so that the number of times each index appears equals the given row total. This vector is then randomly permuted and used to increment the entries in each row so that the given row total is attained.

For tables with larger numbers of entries, the method of Patefield (1981) is used. This method can be considerably faster in these cases. The method depends on the conditional probability distribution of individual elements, given the entries in the previous rows. The probabilities for the individual elements are computed starting from their conditional means.

Example¶

In this example, randomTableTwoway is used to generate a two by three table with row totals 3 and 5, and column totals 2, 4, and 2.

from numpy import *
from pyimsl.stat.randomTableTwoway import randomTableTwoway
from pyimsl.stat.randomSeedSet import randomSeedSet
from pyimsl.stat.writeMatrix import writeMatrix

nrow = 2
ncol = 3
nrtot = [3, 5]
nctot = [2, 4, 2]
randomSeedSet(123457)
itable = randomTableTwoway(nrtot, nctot)
title = "A random contingency table with fixed marginal totals"
writeMatrix(title, itable,
            noRowLabels=True, noColLabels=True)

Output¶

 
A random contingency table with fixed marginal totals
                  0            2            1
                  2            2            1