BUILT-IN MATHEMATICA SYMBOL

# ParetoDistribution

represents a Pareto distribution with minimum value parameter k and shape parameter .

ParetoDistribution[k, , ]
represents a Pareto type II distribution with location parameter .

ParetoDistribution[k, , , ]
represents a Pareto type IV distribution with shape parameter .

## DetailsDetails

• The probability density for value in a Pareto distribution is proportional to for , and is zero for . »
• ParetoDistribution includes Pareto distributions of types I, II, III, and IV:
•  ParetoDistribution[k,] Pareto type I distribution ParetoDistribution[k,,] Pareto type II distribution ParetoDistribution[k,1,,] Pareto type III distribution ParetoDistribution[k,,,] Pareto type IV distribution
• ParetoDistribution[k, , 0] is also known as Lomax distribution.
• The survival function for value in a Pareto distribution corresponds to:
•  ParetoDistribution[k,] ParetoDistribution[k,,] ParetoDistribution[k,,,]
• ParetoDistribution allows k, , and to be any positive real numbers and any real number.
• ParetoDistribution can be used with such functions as Mean, CDF, and RandomVariate. »

## ExamplesExamplesopen allclose all

### Basic Examples (12)Basic Examples (12)

Probability density function for Pareto I:

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Cumulative distribution function for Pareto I:

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Mean and variance of a Pareto I distribution:

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Median of a Pareto I distribution:

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Probability density function for Pareto II:

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Cumulative distribution function for Pareto II:

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Mean and variance of a Pareto II distribution:

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Median of a Pareto II distribution:

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Probability density function for Pareto IV:

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Cumulative distribution function for a Pareto IV distribution:

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Mean and variance of a Pareto IV distribution:

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Median of a Pareto IV distribution:

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