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Statistics[Distributions][Pareto] - Pareto distribution

Calling Sequence

Pareto(a, c)

ParetoDistribution(a, c)

Parameters

a

-

location parameter

c

-

shape parameter

Description

• 

The Pareto distribution is a continuous probability distribution with probability density function given by:

ft&equals;piecewiset<a&comma;0&comma;cactc&plus;1

  

subject to the following conditions:

0<a&comma;0<c

• 

Note that the Pareto command is inert and should be used in combination with the RandomVariable command.

Examples

withStatistics&colon;

X:=RandomVariableParetoa&comma;c&colon;

PDFX&comma;u

&lcub;0u<acacuc&plus;1otherwise

(1)

PDFX&comma;0.5

&lcub;0.0.5<acac0.5c&plus;1.otherwise

(2)

MeanX

&lcub;undefinedc1ca1&plus;cotherwise

(3)

VarianceX

&lcub;undefinedc2ca21&plus;c22&plus;cotherwise

(4)

See Also

Statistics, Statistics[Distributions], Statistics[RandomVariable]

References

  

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

  

Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

  

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.


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