Which equation does Matlab use to fit a Normal distribution?
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Which equation does Matlab use to fit a Normal distribution?, especially for fitdist(x,'Normal') function. I would like to know if the fitting is given by:
or by another expression.
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Matt J
2021-2-11
编辑:Matt J
2021-2-11
To reverse engineer, we can fit the following data
x=randn(1e5,1)*2+5;
which is definitely distributed according to the first density parametrization that you posted (what I would consider the classical parametrization) with mu=5 and sigma=2. Since the routine gives us virtually the same sigma and mu as what we simulated, there is a good chance that the parametric model is the classical one:
pd = fitdist(x,'Normal')
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Matt J
2021-2-12
You're welcome, but please Accept-click an answer that you deem best solves your question.
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John D'Errico
2021-2-11
I think you misunderstand, as there are several things happening here.
A normal distribution fit, that is, finding the parameters of a Normal PDF assumes the distribution has the property that the integral of that function is 1. A PDF has that property, and this is implicit in tools like fitdist.
However, IF you use some other software to perform a nonlinear regression fit, to a model as you show, thiis is NOT a normal distribution. It fails the property that the integral of that function is 1. In fact, the integral from -inf to inf is unbounded, if y0 is ANY number other than zero.
So it is NOT a normal distribution. You may call it a Gaussian fit, but the only thing it has in common with a normal distribution is it looks like a normal, and it is based on the same equation, though perhaps with some additional parameters. It is NOT a normal distribution.
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