Dear Salvatore, Assuming that you mean "convolution" when you write "additive linkage", the answer is that there is no general answer. It will depend heavily on the joint distribution of the two random variables.
Just to give a simple example, let X~f, Y~g, and P(X=0.4)=P(Y=0.4)=1. Then, X and Y are independent, their medians are <0.5, but there sum has a median >0.5. Its different for "multiplicative", since in general from X~f, Y~f, P(X>=0.5)<=0.5, and P(Y>=0.5)<=0.5 it follows that P(XY>=0.5) <= P(X>=p or Y>=q) if p*q=0.5. Thus, if there are numbers p and q with that property, such that P(X>=p) + P(Y>=q) <= 0.5, then the median of XY will be <=0.5. You might argue that there is a relationship between additive and multiplicative scale through a log-transformation (note that the median is stable under monotone transformations). However, I assume there is no obvious formulation of the above statement on the additive scale. There is no way of carrying convolutions out in R directly; you'd need to do numerical integration to do that, e.g. using integrate(). HTH Thomas --- Thomas Hotz Research Associate in Medical Statistics University of Leicester United Kingdom Department of Epidemiology and Public Health 22-28 Princess Road West Leicester LE1 6TP Tel +44 116 252-5410 Fax +44 116 252-5423 Division of Medicine for the Elderly Department of Medicine The Glenfield Hospital Leicester LE3 9QP Tel +44 116 256-3643 Fax +44 116 232-2976 > -----Original Message----- > From: Salvatore Barbaro [mailto:[EMAIL PROTECTED] > Sent: 24 July 2003 12:56 > To: [EMAIL PROTECTED] > Subject: [R] median and joint distribution > > > 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