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From Ted Dunning <ted.dunn...@gmail.com>
Subject Re: [Math] Levenberg Marquardt Help
Date Mon, 31 Jan 2011 03:23:30 GMT
```OK.

Are the data you have samples from this normal distribution?

I.e. are the samples you have from a truncated normal distribution where you
don't know the truncation point exactly?

Or do you actually have a truncated curve?

In the former case, I would define three parameters, mean, standard
deviation and truncation point.  Mean is unconstrained, standard deviation
is bounded to be positive and truncation is bounded to be equal to or larger
than you largest sample.  Then use almost any optimization technique to
minimize maximum absolute deviation of you empirical cumulative distribution
versus the computed version of the truncated distribution.  This should be a
very well behaved optimization that doesn't need any gradient information to
succeed.

On Sun, Jan 30, 2011 at 7:11 PM, Ole Ersoy <ole.ersoy@gmail.com> wrote:

> It's a pretty unique case I agree.  Long story, but I basically have the
> start of what is a normal distribution (Sometimes I get to the top of the
> bell and sometimes I get a 1/3 of the way).  So I'd like to find the best
> fit mean and variance for the set of points.  I'm reading up on numerical
> differentiation, etc. but I'm hoping there's some sort of ABC approach to
> using the LM Optimizer, otherwise it's going to be a long night :).
>
> On 01/30/2011 07:30 PM, Ted Dunning wrote:
>
>> Do you actually need an optimizer for this?  What happened to computing
>> the
>> mean and standard deviation and using those?
>>
>>
>> On Sun, Jan 30, 2011 at 5:08 PM, Ole Ersoy<ole.ersoy@gmail.com>  wrote:
>>
>>  Hi,
>>>
>>> I'm trying to fit a normal distribution to a curve (I'm assuming the LM
>>> Optimizer is a good tool for this).  Is there a generic approach that
>>> lets
>>> me construct a Jacobian or do I need specialized knowledge of the
>>> function
>>> in order to do this?
>>>
>>> TIA,
>>> - Ole
>>>
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>>
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>

```
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