estimate the parameters of lognormal distribution by the some values of CDF
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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
5 Comments
John D'Errico
on 9 Feb 2019
Edited: John D'Errico
on 9 Feb 2019
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
on 9 Feb 2019
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?
Answers (3)
Star Strider
on 9 Feb 2019
Edited: Star Strider
on 9 Feb 2019
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)
EDIT — Added plot figure.
1 Comment
Star Strider
on 9 Feb 2019
@Alon Urlainis —
If my Answer helped you solve your problem, please Accept it!
John D'Errico
on 9 Feb 2019
Looks like this does reasonably well to me.
fplot(@(x) logncdf(x,-.4,.75),[0,2])
hold on
plot(x,y,'.')
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