Lognormal distribution

$mean=e^{a+0.5b^2}$ $variance=e^{2a+b^2}*(e^{b^2}-1)$ $pdf(x) = \frac{1}{\sqrt{2\pi}bx} \exp{(-\frac{1}{2b^2}*{(ln(x)-a)}^2)}$

where $x>=0$

Two parameters: $a$ , location; $b > 0$ its scale.

Lognormal probability distribution

Code to reproduce this plot in octave:

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11 p=lognpdf([0:0.1:3],1,1);
plot(p);
axis([0,33,0,0.3]);
title("Log normal probability distribution");
for i=1:7
    xl{i}=num2str(x((i-1)*5+1));
end
xl{8} = ' ';
set(gca, 'XTicklabel', xl);
print('lnpdf.ps', '-dpsc2');
# convert lnpdf.ps -trim -resize 70% lnpdf.png