Re: Obtaining densest x% of a Bivariate Distribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg127482] Re: Obtaining densest x% of a Bivariate Distribution*From*: Tomas Garza <tgarza10 at msn.com>*Date*: Sat, 28 Jul 2012 02:40:40 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net*References*: <20120726073625.E3F626881@smc.vnet.net>

Well, to start with, BinomialDistribution is not a bivariate distribution. Second, a polygon is always a connected region (if that's what you mean by continuous region). Now, if you mean a univariate distribution, such as the binomial, then I would guess you are looking for the shortest interval in the support of the distribution which encloses x% of the probability. You won't find an interval that satisfies this condition for an arbitrary x. Take, for instance, BinomialDistribution[50, 0.5], and tabulate it for a number of integral intervals. There is no interval which encloses precisely 95% of the probability. Clear[f]; f[k_]:=CDF[BinomialDistribution[50, 0.5], k]; Then take a close look at the following table: Table[{{j, k}, f[k]-f[j]},{j,10,22},{k,30,41}] -Tomas > From: scottfr at gmail.com > Subject: Obtaining densest x% of a Bivariate Distribution > To: mathgroup at smc.vnet.net > Date: Thu, 26 Jul 2012 03:36:25 -0400 > > Hi, > > If I have a bivariate distribution such as, > > BinomialDistribution[50, .5] > > How do I obtain the polygon that encloses that densest x% of the > distribution. For example, what Mathematica functions would I use to > get the most compact polygon (which may or may not be a continuous > region and may or may not contain holes) that encloses 95% of the mass > of a bivariate normal distribution or a bivariate mixture function. > > Thank you, > Scott >

**References**:**Obtaining densest x% of a Bivariate Distribution***From:*Scott Fortmann-Roe <scottfr@gmail.com>