# How to fit lognormal distribution on my data

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Behrooz Daneshian on 15 Nov 2022
Edited: Jeff Miller on 18 Nov 2022
Hi all,
I have 2 vectors. One is the radious of pores within the soil and other is the number of those pores(frequency). Can anyone help me how I can fit a lognormal distribution to these data?

Jeff Miller on 17 Nov 2022
If the scores are in vector1 and the counts are in vector 2, you could fit like this by the method of moments (should be OK with a large dataset):
probs = vector2 / sum(vector2); % Convert counts to probabilities
ExpOfY = sum(vector1.*probs); % mean of the scores tabulated in vectors 1 & 2
Ysqr = vector1.^2;
ExpOfYsqr = sum(Ysqr.*probs);
VarOfY = ExpOfYsqr - ExpOfY^2; % variance of the scores tabulated in vectors 1 & 2
normu = log(ExpOfY/sqrt(1+VarOfY/ExpOfY^2));
norvar = log(1+VarOfY/ExpOfY^2);
norsigma = sqrt(norvar);
dist = makedist('Lognormal','mu',normu,'sigma',norsigma);
x = linspace(0.1,20); % Use whatever range is appropriate for your data
pdfOfx = pdf(dist,x);
figure; plot(x,pdfOfx);
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Jeff Miller on 17 Nov 2022
Edited: Jeff Miller on 18 Nov 2022
Part of the problem is that the red and blue curves are scaled differently. To make them comparable, you need to make them have the same total area under the two curves. The area under the fitted lognormal is 1, but the area under the red curve is clearly much smaller. I think need something like:
vector2nor = vector2 / trapz(vector1,vector2);
plot(vector1,vector2nor);
Also, it does not look like the lognormal is actually a very good fit, because the two curves have pretty different shapes (blue descends much more than red across the last 6 tics before 10^-4).

David Hill on 15 Nov 2022
Look at lognfit
[pHat,pCI] = lognfit(repelem(vector1,vector2));
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David Hill on 16 Nov 2022
if all the frequencies are of the same order of magnitude, you could scale them all down.