The Iman Conover method induces correlation between given marginal distributions by appropriately shuffling
each marginal. Positive correlation is induced by a tendency to shuffle larger values together, negative correlation
by combining smaller losses from one marginal with larger losses from the other.
The shuffle is determined by ranking the input marginals the same as a sample with the desired correlation.
Thus, strictly, the method gives the desired rank correlation, not Pearson correlation.
For reasonably symmetric distributions the approximation is very good. For more skewed distributions
there is a greater difference.
The "test" sample
is computed in the usual way by applying the Choleski decomposition of the correlation matrix to a random sample
of scores. Iman and Conover's method adjusts for the random correlation in the score distribution.
The method can produce radically different contour
plots depending on the distribution used for the scores. Selecting a normal
score type results in elliptical contours. Selecting uniform or exponential
scores will produce very different countour plots.
References
Iman, Ronald L. and W. J. Conover, A Distribution-Free Approach to Inducing Rank Correlation
Amoung Input Variables, Commun. Statist.-Simula. Computation 11(3), pp. 311-334 (1982)
Vitale, R. A. On Stochastic Dependence and a Class of Degenerate Distributions, in Topics in
Statistical Dependence, ed. Henry W. Block, Allan R. Sampson and Thomas H. Savits, Institiute of
Mathematical Statistics, Hayward CA (1990)
