How to fit lognormal distribution on my data

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Behrooz Daneshian 2022-11-15

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编辑： Jeff Miller 2022-11-18

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?

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Answer 1

Jeff Miller 2022-11-17

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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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Behrooz Daneshian 2022-11-17

PDFS.JPG

Thank you Jeff for your reply. I did exacly what you recommended to do. However, the results seems weird to me. Please look at the attached picture. The red plot belongs to radious(vector1) vs frequency(vector2) and the blue plot is for fitted lognormal pdf. Can you see the huge discrepency between the two curves?

Jeff Miller 2022-11-17

编辑：Jeff Miller 2022-11-18

在 MATLAB Online 中打开

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).

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