How can I fit histogram?

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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'?

Accepted Answer

the cyclist
the cyclist on 30 Oct 2021
Edited: the cyclist on 30 Oct 2021
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
  2 Comments
the cyclist
the cyclist on 1 Nov 2021
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))

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