Peng Jiang wrote: > Hi, xiechao > i don't think that is a R specific problem. you mean u got two random > variables X,Y and both > of them binomial distributed and you want to find the distribution of > a new variable Z = X/Y. > That is a basic transformation problem. u can start with introducing a > new r.v. namely W, by > letting it equal to X you obtain W=X,Z=X/Y from which u have X = W > and Y = W / Z. It is easy > to find the Jacobian of this transformation, and the left is routinely. Not that easy! X and Y are discrete, and the result is an improper distribution since there is a positive probability of dividing by 0. If the mean of X and Y are moderately large, the delta method can be used. If they have a small(-ish) number of different values, I'd be tempted just to use brute force, as in
r <- outer(x,y,"/") r[0,0] <- 0 # 0/0 defaults to NaN p <- outer(dbinom(x,10,.5), dbinom(y,10,.5)) o <- order(r) plot(r[o],cumsum(p[o]), type="s") plot(unique(r[o]),tapply(p[o],list(r[o]), sum), type="h") (the latter plot is not quite right --- should take better care of rounding issues) > > regards. > On 2008-6-27, at 下午8:29, Xie Chao wrote: > >> Hi all, >> >> I am a biological student and need your help in statistics. >> >> I have two sets of binomial distributed numbers: {a1, a2, ..., an} >> and {b1, >> b2, ..., bn}. >> How can I get the distribution of the ratios of the two sets of numbers >> {a1/b1, a2/b2, ..., an/bn}? Is there a formula to transform the >> distributions? Or where I can start if I want to learn necessary >> techniques? >> Thank you a lot! >> >> xiechao >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. > > ----------------------------------------------- > Peng Jiang > 江鹏 > Ph.D. Candidate > Antai College of Economics & Management > 安泰经济管理学院 > Department of Mathematics > 数学系 > Shanghai Jiaotong University (Minhang Campus) > 800 Dongchuan Road > 200240 Shanghai > P. R. China > > ______________________________________________ > R-help@r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide > http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code. -- O__ ---- Peter Dalgaard Øster Farimagsgade 5, Entr.B c/ /'_ --- Dept. of Biostatistics PO Box 2099, 1014 Cph. K (*) \(*) -- University of Copenhagen Denmark Ph: (+45) 35327918 ~~~~~~~~~~ - ([EMAIL PROTECTED]) FAX: (+45) 35327907 ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.