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ParetoDistribution
ParetoDistribution[k, 
]
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 .
Details
- 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. »
Examplesopen all
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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