estimate the parameters of lognormal distribution by the some values of CDF

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Alon Urlainis
Alon Urlainis 2019-2-9
评论： Star Strider 2019-2-9
hello,
I want to find estimate the parameters of lognormal distribution by the some values of CDF
for example:
x= [0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00]
y= [0.000 0.000 0.005 0.022 0.051 0.091 0.138 0.188 0.240 0.291 0.341 0.389 0.434 0.476 0.515 0.552 0.586 0.617 0.646 0.672 0.696 0.719 0.739 0.758 0.776 0.792 0.806 0.820 0.832 0.844 0.854 0.864 0.873 0.881 0.889 0.896 0.903 0.909 0.915 0.920 0.925]
I want to estimate the mu and beta of the lognormal parameters
thanks
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John D'Errico
John D'Errico 2019-2-9
编辑：John D'Errico 2019-2-9
Assuming this is the CDF, then it is close to complete, just missing part of the upper tail. The PDF would go down, but not the CDF.
Image Analyst
Image Analyst 2019-2-9
I know. So give us the PDF since it's the PDF that has the log normal shape.
I know we can get it from the CDF but why not make it EASY for us to help you, not hard?

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回答（3 个）

Star Strider
Star Strider 2019-2-9
编辑：Star Strider 2019-2-9
Try this:
fcn = @(b,x) cdf('Lognormal',x,b(1),b(2));
x= [0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75 1.80 1.85 1.90 1.95 2.00];
y= [0.000 0.000 0.005 0.022 0.051 0.091 0.138 0.188 0.240 0.291 0.341 0.389 0.434 0.476 0.515 0.552 0.586 0.617 0.646 0.672 0.696 0.719 0.739 0.758 0.776 0.792 0.806 0.820 0.832 0.844 0.854 0.864 0.873 0.881 0.889 0.896 0.903 0.909 0.915 0.920 0.925];
[B,resnorm] = fminsearch(@(b) norm(y - fcn(b,x)), [1; 1]);
evf = fcn(B,x);
figure
plot(x, y, '.')
hold on
plot(x, evf, '-r')
hold off
grid
text(median(x), median(y)/2, sprintf('\\mu = %6.3f\n\\sigma = %6.3f', B))
EDIT — (9 Feb 2019 at 19:06)
estimate the parameters of lognormal distribution by the some values of CDF - 2019 02 09.png
EDIT — Added plot figure.
John D'Errico
John D'Errico 2019-2-9
Looks like this does reasonably well to me.
fplot(@(x) logncdf(x,-.4,.75),[0,2])
hold on
plot(x,y,'.')
untitled.jpg
Alon Urlainis
Alon Urlainis 2019-2-9
Thank you
Works great !!!

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