Normalized histogram with gaussian fit

Hi, I know how to make an histogram and make it so it is normalized according to the probability

histogram(x, nbits, 'Normalization','probability')

and also how to fit a gaussian curve to the histogram: histfit (x)

But if I use the command histfit I don't know how to normalize it according to the probability.

I would like to have both, a normalized histogram with the probability, that also has the plot of the gaussian distribution that fits to my data set.

I hope my question is clear and that you can help me :)

Answer 1

[Alan Stevens]

Here's an example showing one possibility:

gaussian = @(x, m,s) exp(-0.5*((x-m)/s).^2)/(s*sqrt(2*pi));

mu = 5;                             % Arbitrary mean
sigma = 1;                          % arbitrary standard deviation
x = mu + sigma*randn(1,400);   % Arbitrary random normal data

h = histogram(x);
dh = h.BinWidth;
lo = min(x);
hi = max(x);
dxx = (hi-lo)/100;
xx = linspace(lo,hi,101);
pdf = gaussian(xx, mu, sigma);
scalefactor = sum(h.Values*dh)/(trapz(pdf)*dxx);
pdf = scalefactor*pdf;
hold on
plot(xx,pdf)

[Miquel Vega Paredes]

Thank you so much for your help! :)

[studentmatlaber]

@Alan Stevens I ran the code you wrote. But shouldn't the normalized histogram be between 0 and 1?

[Alan Stevens]

The AREA under the curve should be 1.