Mean of general Beta distribution
in [Matlab]
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From: John D'Errico on 5 Jul 2010 08:21 "Wayne King" <wmkingty(a)gmail.com> wrote in message <i0sgk2$gc5$1(a)fred.mathworks.com>... > "Ulrik Nash" <uwn(a)sam.sdu.dk> wrote in message <i0seie$4a3$1(a)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). Actually, this is not true. There are many who use a 4 parameter beta distribution, wherein the 3rd and 4th parameters are the lower and upper limits of the distribution support. It is a simple shift and scale transformation from the standard beta. And of course, a beta distribution is based on a shifted incomplete beta function anyway, so it is already really a transformation based on a shift and scale. I'll bet this is discussed in the bible of distributions, i.e., Johnson, Kotz, & Balakrishnan. John
From: Wayne King on 5 Jul 2010 08:56
"John D'Errico" <woodchips(a)rochester.rr.com> wrote in message <i0sing$37i$1(a)fred.mathworks.com>... > "Wayne King" <wmkingty(a)gmail.com> wrote in message <i0sgk2$gc5$1(a)fred.mathworks.com>... > > "Ulrik Nash" <uwn(a)sam.sdu.dk> wrote in message <i0seie$4a3$1(a)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). > > Actually, this is not true. > > There are many who use a 4 parameter beta distribution, > wherein the 3rd and 4th parameters are the lower and > upper limits of the distribution support. It is a simple > shift and scale transformation from the standard beta. > > And of course, a beta distribution is based on a shifted > incomplete beta function anyway, so it is already really > a transformation based on a shift and scale. > > I'll bet this is discussed in the bible of distributions, > i.e., Johnson, Kotz, & Balakrishnan. > > John Sorry all, I stand corrected. Thanks for the info! Wayne |