For distribution functions F and G we have the (Frechet) bounds: max{0, F(x)+G(y) -1} <= H(x,y) <= min{F(x),F(y)}
where H is the joint df of (X,Y) having marginals F and G. If X and Y are comonotonic (Schmeidler (Econometrica, 1989)), that is if there is a random variable Z, such that X = f(Z), and Y=g(Z) for monotone f and g, then the upper Frechet bound holds and the quantile function of X+Y is the sum of the quantile functions of X and Y. For "multiplicative linkage" take logs, presuming, of course, that I'm not misinterpreting this phrase. One can think of comonotone X and Y as "perfectly concordant" in the language of rank correlation. url: www.econ.uiuc.edu/~roger/my.html Roger Koenker email [EMAIL PROTECTED] Department of Economics vox: 217-333-4558 University of Illinois fax: 217-244-6678 Champaign, IL 61820 On Thu, 24 Jul 2003, Salvatore Barbaro wrote: > Dear R-"helpers"! > > May I kindly ask the pure statistics-experts to help me for a > purpose which first part is not directly concerned with R. > Consider two distribution functions, say f and g. For both, the > median is smaller than a half. Now, the multiplicative or additive > linkage of both distribution leads to a new distribution function, > say h, whereas the median of h is greater than a half. Does > anybody know under which circumstances such a construction of h is > possible (my intuition is that it depends on the correlation of f > and g) or can anybody advice a helpful literature. Furthermore, > does anybody know whether or how such a construction can be done > with R. Thanks in advance. > > s. > > ______________________________________________ > [EMAIL PROTECTED] mailing list > https://www.stat.math.ethz.ch/mailman/listinfo/r-help > ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help