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Re: partitioning into equiprobable intervals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41058] Re: [mg41013] partitioning into equiprobable intervals
  • From: Bobby Treat <drmajorbob+MathGroup3528 at mailblocks.com>
  • Date: Wed, 30 Apr 2003 04:24:13 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Here are a couple of loops, depending on what form the answer should be 
in.

<< Statistics`NormalDistribution`
mean = 2.1; sigma = 1.5;
dist = NormalDistribution[mean, sigma];
pdf = PDF[dist, x]
cdf = CDF[dist, #] &;
n = 10;
N@Table[Quantile[dist, k/n], {k, 0, n}]
low = -Infinity;
intervals = Table[{low, low = Quantile[dist, k/n]}, {k, 1, n}];
N@intervals

and here's a colorful plot of the result.

<< Graphics`Graphics`
<< Graphics`FilledPlot`
Off[$MaxExtraPrecision::"meprec"]
nSig = 5;
{low, high} = mean + nSig*sigma{-1, 1}/2;
DisplayTogether[intervals /. {a_, b_} :> {Max[a, low], Min[b, high]} /. 
{a_,
    b_} :> FilledPlot[pdf, {x, a, b}, Fills -> {Hue@cdf@b}]];

Hue can be replaced by GrayLevel.  Changing "mean" and "sigma" changes 
everything, and "nSig" is the number of standard deviations to be 
plotted.

Bobby

-----Original Message-----
From: susanlcw at aol.com
To: mathgroup at smc.vnet.net
Subject: [mg41058] [mg41013] partitioning into equiprobable intervals

Hi all,

I am interested in taking a normal distribution with mean and standard
deviation known, and partitioning it into n equiprobable intervals.
This means that the area under the curve on each interval will be 1/n.
I know how to define the pdf, but I am at a loss as to how to design
some type of loop (?) that will accomplish this task.

I would greatly appreciate any suggestions.
Thanks,
Susan


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