ParetoDistribution

ParetoDistribution[k,α]
represents a Pareto distribution with minimum value parameter k and shape parameter α.

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

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

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,α]Pareto type I distribution
    ParetoDistribution[k,α,μ]Pareto type II distribution
    ParetoDistribution[k,1,γ,μ]Pareto type III distribution
    ParetoDistribution[k,α,γ,μ]Pareto type IV distribution
  • ParetoDistribution[k,α,0] is also known as Lomax distribution.
  • The survival function for value in a Pareto distribution corresponds to:
  • ParetoDistribution[k,α]
    ParetoDistribution[k,α,μ]
    ParetoDistribution[k,α,γ,μ]
  • ParetoDistribution allows k, α, and γ to be any positive real numbers and μ 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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Introduced in 2007
(6.0)
| Updated in 2010
(8.0)