How can I fit histogram?

I want to normalize my histogram. I know there are commands histogram(x, nbits, 'Normalization','probability') and histogram(x, nbits, 'Normalization','pdf'). But what is the difference between 'probability' and 'pdf'?

Answer 1

[the cyclist]

Answering the first part of your question ...

With probability normalization, the sum of the bin heights will be 1. With pdf normalization, the integral of the bins (i.e. the sum of the bin heights times widths) will be 1.

Here is a silly example that illustrates the difference:

rng default
N = 5000;
x = binornd(1,0.5,N,1)/2;

figure
histogram(x, 5, 'Normalization','probability')

figure
histogram(x, 5, 'Normalization','pdf')

Answering the second part of your question ...

I believe you can use histcounts to get the normalized bin counts, then fit those values with normfit:

[binCounts, binEdges] = histcounts(x, 5, 'Normalization','probability');
binCenters = (binEdges(1:end-1) + binEdges(2:end))/2;
[muHat,sigmaHat] = normfit(binCenters,binCounts)

muHat = 0.2500

sigmaHat = 0.1581

[studentmatlaber]

Thank you very much for your reply. However, after finding the mean and sigma values with the normfit, how do I draw the fit graph of it? I have uploaded my file in the question. I fit the histogram with "t location scale" with distribution fitter app. However I want to normalize it as "probability". I can find the mean and sigma value as you suggested, but how do I plot it later? I couldn't picture it in my head. I would be glad if you help.

[the cyclist]

You need to plot it according to the formula for a normal distribution. (See, e.g., this wikipedia page.)

You could just code that formula from scratch, but instead you could create a distribution object:

mu = 2;
sigma = 3;

pd_norm = makedist('Normal','mu',mu,'sigma',sigma)

pd_norm = 
  NormalDistribution

  Normal distribution
       mu = 2
    sigma = 3

x = -3:0.01:7;
plot(x,pdf(pd_norm,x))