Path: news.mathworks.com!newsfeed-00.mathworks.com!kanaga.switch.ch!switch.ch!feeder.news-service.com!85.214.198.2.MISMATCH!eternal-september.org!.POSTED!not-for-mail From: <HIDDEN> Newsgroups: comp.soft-sys.matlab Subject: Re: Mean of general Beta distribution Date: Mon, 05 Jul 2010 07:06:36 -0500 Organization: A noiseless patient Spider Lines: 34 Message-ID: <i0si1b$ac7$1@news.eternal-september.org> References: <i0seie$4a3$1@fred.mathworks.com> <i0sgk2$gc5$1@fred.mathworks.com> Mime-Version: 1.0 Content-Type: text/plain; charset=UTF-8; format=flowed Content-Transfer-Encoding: 7bit Injection-Date: Mon, 5 Jul 2010 12:09:16 +0000 (UTC) Injection-Info: mx02.eternal-september.org; posting-host="9ZCs6V+grFf9UjsifTbvJA"; logging-data="10631"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1/P9ejhGhsnIFcGWwXWQMPU" User-Agent: Thunderbird 2.0.0.24 (Windows/20100228) In-Reply-To: <HIDDEN> Cancel-Lock: sha1:B36hk24YbyX+JOSHNJemh9uTcEo= Xref: news.mathworks.com comp.soft-sys.matlab:650435 Wayne King wrote: > "Ulrik Nash" <uwn@sam.sdu.dk> wrote in message > <i0seie$4a3$1@fred.mathworks.com>... >> Hi Everyone, >> >> This is I suppose is more a general maths question. >> I am working on a simulation where I would like to specify the upper >> and lower bounds of the Beta distribution, and at the same time be >> able to directly set the mean of the distribution, instead of >> indirectly via the shape parameters. I am aware of the mean of the >> Beta distribution, but only for lower and upper limits of 0 and 1. >> What is the general equation for the mean, involving the two shape >> parameters and the upper and lower limits of the distribution? >> >> Best >> >> Ulrik. > > Hi Ulrik, the beta distribution is only defined on the interval (0,1). > The mean of the beta distribution is alpha/(alpha+beta). I'm not quite > sure what you're asking in terms of lower and upper limits. The mean > depends directly on the two parameters and the shape of the resulting > pdf can vary greatly depending on the values you use for alpha and beta. The beta distribution can be generalized to cover the interval (u0,u1) by transformation of variable of [(x-u0)/(u1-u0)] for x. See Hahn & Shapiro, Statistical Models in Engineering, Wiley. I don't have a closed form solution for the expected value and so on otomh, though; whether H&S have the generalized form in summary tables on continuous distributions I don't recall; it's not on the shelf here but would have to go find it :). --