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Statistics[Distributions]

  

Pareto

  

Pareto distribution

 

Calling Sequence

Parameters

Description

Examples

References

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=0t<acactc+1otherwise

  

subject to the following conditions:

0<a,0<c

• 

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

Examples

withStatistics&colon;

XRandomVariableParetoa&comma;c&colon;

PDFX&comma;u

0u<acacuc+1otherwise

(1)

PDFX&comma;0.5

0.0.5<acac0.5c+1.otherwise

(2)

MeanX

undefinedc1ca1+cotherwise

(3)

VarianceX

undefinedc2ca21+c22+cotherwise

(4)

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.

See Also

Statistics

Statistics[Distributions]

Statistics[RandomVariable]