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Re: eqiprobable intervals

  • To: mathgroup at smc.vnet.net
  • Subject: [mg41056] Re: [mg41020] eqiprobable intervals
  • From: Daniel Lichtblau <danl at wolfram.com>
  • Date: Wed, 30 Apr 2003 04:23:58 -0400 (EDT)
  • References: <200304290923.FAA09453@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

susanlcw at aol.com wrote:
> 
> Hi all,
> 
> I am interested in finding a program that will divide the domain of
> a probability density function
> into n non-overlapping equiprobable intervals.  Specifically, I am working
> with a normal distribution, where mean and standard deviation are known
> (and I know how to define the pdf), so the area under the curve on each
> interval would be 1/n.
> 
> Any help would be greatly appreciated.
> Thanks,
> Susan

This will work with any distribution for which Quantile is implemented.

equiprobableIntervals[dist_,n_] :=
  Partition[Table[Quantile[dist,k/n], {k,0,n}], 2, 1]

Example:

<<Statistics`
dist = NormalDistribution[];

In[23]:= intervals = N[equiprobableIntervals[dist,8]]
Out[23]= {{-Infinity, -1.15035}, {-1.15035, -0.67449}, {-0.67449,
-0.318639}, 
  {-0.318639, 0.}, {0., 0.318639}, {0.318639, 0.67449}, 
  {0.67449, 1.15035}, {1.15035, Infinity}}

We check that this is correct.

In[24]:= Map[CDF[dist,#[[2]]]&, intervals]
Out[24]= {0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1}


Daniel Lichtblau
Wolfram Research


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