Which equation does Matlab use to fit a Normal distribution?

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.

[Matt J]

or by another expression.

What other expression?

[Andreina Urquiola]

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.

Answer 1

[Matt J]

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]

[Andreina Urquiola]

Thank you!

[Matt J]

You're welcome, but please Accept-click an answer that you deem best solves your question.

Answer 2

[John D'Errico]

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.

[Andreina Urquiola]

Thank you!