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

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

[Image Analyst]

It's having trouble because you have only half of a log-normal shape. Does it ever go down again?

Looks more like the rate equation. Do you want to fit it to that instead? Or do you know for a fact that it's log-normal?

Is it the CDF that you think is a log normal shape, or the underlying data? If it's the underlying data, then give us that rather than the CDF values.

[Alon Urlainis]

hi,

It only goes up.

I want to make sure that the graph fits a lognormal distribution.

i want to find the lognormal parameters that have best fit to the data

[Alon Urlainis]

Its a CDF data not PDF

[John D'Errico]

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]

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?

Answer 1

[Star Strider]

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.

[Star Strider]

@Alon Urlainis —

If my Answer helped you solve your problem, please Accept it!

Answer 2

[John D'Errico]

Looks like this does reasonably well to me.

fplot(@(x) logncdf(x,-.4,.75),[0,2])
hold on
plot(x,y,'.')

Answer 3

[Alon Urlainis]

Thank you

Works great !!!