© 1967 by Biometrika Trust
Some contributions to contingency-type bivariate distributions
University of Newcastle upon Tyne
Plackett (1965) has given a class of contingency-type bivariate distributions which contains the boundary distributions and the member corresponding to independent random variables. This is the only bivariate class known to possess this important property. In addition, Plackett (1965) has given some interesting applications of these distributions. The class is determined by solving a quadretic equation and discarding one of the roots not satisfying a set of inequalities. In this paper, we obtain the required root. We provide a simple method of drawing random samples from this type of population. We derive the moment-formulae appropriate to this class and apply these to simplify moments of contingency-type normal and uniform distributions. We compare the bivariate normal distribution with the contingency-type bivariate normal, and demonstrate that this latter distribution provides a simple method of computing tetrachoric correlation. We give a new estimate of the coefficient of association and show that the asymptotic efficiency of Plackett's estimate relative to ours, in the region of interest, lies between 46 and 56 %. Another estimate is also considered.