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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)
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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>