| Statistics Toolbox | |
Lognormal Distribution
The following sections provide an overview of the lognormal distribution.
Background of the Lognormal Distribution. The normal and lognormal distributions are closely related. If X is distributed lognormal with parameters µ and 
2, then lnX is distributed normal with parameters µ and 2.
The lognormal distribution is applicable when the quantity of interest must be positive, since lnX exists only when the random variable X is positive. Economists often model the distribution of income using a lognormal distribution.
Definition of the Lognormal Distribution. The lognormal pdf is
Example and Plot of the Lognormal Distribution. Suppose the income of a family of four in the United States follows a lognormal distribution with µ = log(20,000) and 2 = 1.0. Plot the income density.
x = (10:1000:125010)';
y = lognpdf(x,log(20000),1.0);
plot(x,y)
set(gca,'xtick',[0 30000 60000 90000 120000])
set(gca,'xticklabel',str2mat('0','$30,000','$60,000',...
'$90,000','$120,000'))
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