fitting gaussian distribution to data

Question

I have a vector y containing 1440 values (values are between 0-1) that looks like a Gaussian distribution. Therefore I would like to find the best fitting gaussian distribution to have a model.

x=1:1440;
[sigma_,mu_] = gaussfit(x,y);
norm = normpdf(x,mu_,sigma_);

My problem is that the values in norm are way smaller than the values in y, i.e. value in norm are of the order of 10-3 while values in y are between 0 1.

I have then to add an extra step in order to normalize between 0 and 1 the values in norm.

norm_data = (norm - min(norm)) / ( max(norm) - min(norm) );

Is my procedure correct? (estimation of sigma and mu, normpdf, normalization) Is there a way to get directly a fit to the original data expressing the probability?

y can be downloaded here

Answer 1

Assuming you are using this gaussfit, if you check the head of the function:

% REMARKS:
% The function does not always converge in which case try to use initial
% values sigma0, mu0. Check also if the data is properly scaled, i.e. p.d.f
% should approx. sum up to 1

Which means that before fitting you need to make sure that sum(y)==1+err being err something small.

Your y has a sum(y) of 470.1964, which is kind of far from 1. Normalize your data so the sum is equal to one before fitting it.

EDIT

Indeed the fucntion does normalize if the data is not (more or less, it accepts data in range 0.5-1.5). And works perfectly fine. As y is normalized inside the function, If you want to compare the result norm to y you need to normalize y or denormalize norm.

 % normalize y
 plot(x,norm,x,y./sum(y))
 % denormalize norm
 plot(x,norm*sum(y),x,y)

in either case (but different scale):

Answer 2

gaussfit(x,y) fits a normalized Gaussian to the data. If your data is not normalized this cannot work. The question of how to fit it properly is answered here!