Re: Fitting NormalDistribution to 2D List

• To: mathgroup at smc.vnet.net
• Subject: [mg31459] Re: Fitting NormalDistribution to 2D List
• From: post_12 at hotmail.com (postman)
• Date: Wed, 7 Nov 2001 05:29:30 -0500 (EST)
• References: <9s1uhd\$o4b\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```BobHanlon at aol.com wrote in message news:<9s1uhd\$o4b\$1 at smc.vnet.net>...
> Needs["Statistics`NormalDistribution`"];
> Needs["Statistics`DescriptiveStatistics`"];

Bob:

This was very helpful, thanks for taking the time to post. I still
haven't got my head around the use of symbols like # and & in

While the code you posted solves the specific example I asked about, I
am still unable to fit my data to an arbitrary distribution (e.g.
ExtremeValue, LaPlace). Is there a way to pass these distributions and
my Tables of data to the Nonlinear fitting algorithm? Unrolling is
unfortunately not an option; my machine (1GB RAM) ran out of memory
trying to unroll 1 data set.

Thanks again for your help -

>
> data={{1,2},{2,8},{3,16},{4,7},{5,3}};
>
> unrolledData = Flatten[Table[#[[1]],{#[[2]]}]& /@data];
>
> mu = Mean[unrolledData];
>
> To find the mean without unrolling
>
> mu==(Plus@@(Times@@#& /@ data))/(Plus@@data[[All,2]])
>
> True
>
> or
>
> mu==Tr[Times@@#& /@ data]/Tr[data[[All,2]]]
>
> True
>
> or
>
> mu==(Dot@@Transpose[data])/Tr[data[[All,2]]]
>
> True
>
> Selecting a method
>
> binnedMean[data_] := Tr[Times@@#& /@ data]/Tr[data[[All,2]]];
>
> m = binnedMean[data];
>
> The StandardDeviationMLE of the data without "unrolling" is
>
> s = Sqrt[binnedMean[{(#[[1]]-m)^2, #[[2]]}& /@ data]];
>
> s == StandardDeviationMLE[unrolledData]
>
> True
>
> The distribution is
>
> NormalDistribution[m, s]
>
> NormalDistribution[109/36,
>   Sqrt[1259]/36]
>
>
> Bob Hanlon
> Chantilly, VA  USA

```

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