pareto

PDF
CDF
Mode

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.

Samples 

pareto(double alpha, double min)

Description

Generates a sample of the Pareto distribution.

Parameters

Name Type 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 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 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