> Rolf, > > > On Wed, 2008-04-09 at 10:57 +1200, Rolf Turner wrote: >> On 9/04/2008, at 10:30 AM, Phil Rhoades wrote: >> >> > People, >> > >> > Say a particular measure of an attribute for individuals in different >> > populations gives a set of overlapping normal distributions (one >> > distribution per population). If I then measure this attribute in >> > a new >> > individual - how do I assess the likelihood of this new individual >> > belonging to each of the different populations? >> >> You have a mixture of distributions. Let the density be >> >> k >> f(x) = SUM lambda_i * f_i(x) >> i=1 >> >> where the f_i(x) are the densities for the individual components in >> the mixture, >> and the lambda_i are the mixing probabilities. >> >> The probability that an individual with observation x is from >> component i is >> >> lambda_i * f_i(x) >> ----------------- >> f(x) > > > Thanks for the quick response but I think I need to put some numbers on > this so I can see what you mean. Say I have two pops with individual > values: > > 1 2 3 4 5 > > 3 4 5 6 7 > > and a new individual with value 5 - what is the likelihood of assignment > to each of the populations?
Phil, for an application and more detailed explanation you can check the article: A Test for Long-Term Cyclical Clustering of Stock Market Regimes John Powell, Rubén Roa, Jing Shi, Viliphonh Xayavong Australian Journal of Management, vol. 32(2), 2007, available for free download from the journal website: http://www.agsm.edu.au/~eajm/current.html I provide there a quotation to a book by Hamilton on time series, where this technique is further explained. By the way, the computation suggested is a conditional probability. Rubén ______________________________________________ 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.
