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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.
  2 Comments
Andreina Urquiola
Andreina Urquiola on 11 Feb 2021
Different expressions can be used to minimize errors. For example Origin (data analysis software) uses this equation to obtain the gaussian fit:
I would like to know which expression is used by Matlab.

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Accepted Answer

Matt J
Matt J on 11 Feb 2021
Edited: Matt J on 11 Feb 2021
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')
pd =
NormalDistribution Normal distribution mu = 4.99612 [4.98373, 5.00851] sigma = 1.99916 [1.99044, 2.00796]

More Answers (1)

John D'Errico
John D'Errico on 11 Feb 2021
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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