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The Pareto distribution is a continuous distribution bounded on the lower side. It has a finite value at the minimum x and decreases monotonically for increasing x. A Pareto random variable is the exponential of an Exponential random variable, and possesses many of the same characteristics.

The Pareto distribution has, historically, been used to represent the income distribution of a society. It is also used to model many empirical phenomena with very long right tails, such as city population sizes, occurrence of natural resources, stock price fluctuations, size of firms, brightness of comets, and error clustering in communication circuits.

The shape of the Pareto curve changes slowly with alpha, but the tail of the distribution increases dramatically with decreasing alpha.

Examples

pareto(double alpha, double min)

Description
Generates a sample of the Pareto distribution.
Parameters
Name Type of value Description
alpha double The scale parameter > 0.
min double The minimum x value.
Result
Type Description
double The generated sample.

pareto(double alpha)

Description

Generates a sample of the Pareto distribution with min set to 1. Is equivalent to pareto(alpha, 1).

Parameters
Name Type of value Description
alpha double the scale parameter > 0.
Result
Type Description
double The generated sample.

pareto(double alpha, double min, java.util.Random r)

Description
Generates a sample of the Pareto distribution using the specified random number generator.
Parameters
Name Type of value Description
alpha double The scale parameter > 0.
min double The minimum x value.
r java.util.Random The random number generator.
Result
Type Description
double The generated sample.

This document includes content from the “Stat::Fit User’s Manual”. Copyright 2016 Geer Mountain Software Corp.

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