       Re: Get Distribution from Interpolated Function

• To: mathgroup at smc.vnet.net
• Subject: [mg128284] Re: Get Distribution from Interpolated Function
• From: Tomas Garza <tgarza10 at msn.com>
• Date: Wed, 3 Oct 2012 23:40:55 -0400 (EDT)
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• References: <20121003070909.A52016881@smc.vnet.net>

```I think the Histogram is working fine. The problem is with randonData, all of whose elements are less than 1.Note that dist is not a probability distribution, since in my example
In:= NIntegrate[PDF[dist, x], {x, 0, 10}]

Out= 13.6285
If you first normalize dist (i.e., divide dist by NIntegrate[PDF[dist, x], {x, 0, 10}]), then you'll get a histogram which more or less resembles the curve form.
--Tomas

> From: rodrigomurtax at gmail.com
> Subject: Get Distribution from Interpolated Function
> To: mathgroup at smc.vnet.net
> Date: Wed, 3 Oct 2012 03:09:09 -0400
>
> Hi All
>
>     I'm trying to get a distribution from an interpolated function but with no success.
>
> (*Creating Dist from interpolation*)
> ff = Interpolation[Table[{i, 1 + RandomReal}, {i, 0, 10, 1}], Method -> "Spline"];
> dist = ProbabilityDistribution[ff[x], {x, 0, 10}];
>
>  (*Plot Interpolation ok!*)
> Plot[ff[x], {x, 0, 10}]
>
> (*Plot Dist ok!*)
> Plot[Evaluate@PDF[dist, x], {x, 0, 10}]
>
> (*do not work as spected, the histogram don't have the curve format*)
> randonData = RandomVariate[dist, 100000];
> Histogram[randonData, {0.1}, "Probability",  PlotRange -> {{0, 10}, All}]
>