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Lognormal Distribution

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Definition Background Example See Also

Definition

The lognormal pdf is

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Background

The normal and lognormal distributions are closely related. If X is distributed lognormally with parameters µ and σ, then log(X) is distributed normally with mean µ and standard deviation σ.

The mean m and variance v of a lognormal random variable are functions of µ and σ that can be calculated with the lognstat function. They are:

A lognormal distribution with mean m and variance v has parameters

The lognormal distribution is applicable when the quantity of interest must be positive, since log(X) exists only when X is positive.

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Example

Suppose the income of a family of four in the United States follows a lognormal distribution with µ = log(20,000) and σ² = 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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See Also

Continuous Distributions (Data)

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Loglogistic Distribution

Multinomial Distribution

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