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scripts default iconrandp.m (Scripts) Publisher's description

This function generates Pareto random variables (of type I)

This function generates Pareto random variables (of type I). See
"Statistical Distributions", Evans, Hastings and Peacock, Wiley, 1993
or http://www.maths.adelaide.edu.au/matthew.r...trns/node6.html
or http://en.wikipedia.org/wiki/Pareto_distribution

The Pareto distribution is a classic "heavy-tailed" or "power-law" distribution. It has distribution function
F(x) = 1 - (b/x)^alpha, for x>=b
and density
f(x) = (alpha/b) * (b/x)^(alpha+1), for x>=b

Its mean is
E[X] = b * alpha/(alpha-1), for alpha>1
but note that the mean is infinite for alpha<=1

Its variance is
Var(X) = b^2 * alpha/[(alpha-1)^2*(alpha-2)], for alpha>1
but note that the variance is infinite for alpha<=2

Median
Med(X) = b * 2^(1/alpha)

Note the function calls "rand" so if you want to control the seed, use rand('state', seed).

Also note that the type II Pareto is just shifted so that x>=0, so to obtain this distributio just take
x = randp(N,M,alpha,b) - b;

System Requirements:

MATLAB 7.4 (R2007a)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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