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Statistics[Distributions]

  

FRatio

  

f-ratio distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

FRatio(nu, omega)

FRatioDistribution(nu, omega)

Parameters

nu

-

first degrees of freedom parameter

omega

-

second degrees of freedom parameter

Description

• 

The f-ratio distribution is a continuous probability distribution with probability density function given by:

ft=0t<0νων2tν211+νtων2+ω2Βν2&comma;ω2otherwise

  

subject to the following conditions:

0<ν,0<ω

• 

The FRatio variate is related to independent ChiSquare variates with degrees of freedom nu and omega by the formula FRatio(nu,omega) ~ (ChiSquare(nu)*omega)/(ChiSquare(omega)*nu)

• 

The FRatio variate is related to independent Laplace variates with location parameter 0 and scale parameter b by the formula FRatio(2,2) ~ abs(Laplace(0,b))/abs(Laplace(0,b))

• 

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

Examples

withStatistics&colon;

XRandomVariableFRatio&nu;&comma;&omega;&colon;

PDFX&comma;u

&lcub;0u<0&Gamma;12&nu;&plus;12&omega;&nu;&omega;12&nu;u12&nu;1&Gamma;12&nu;&Gamma;12&omega;1&plus;&nu;u&omega;12&nu;&plus;12&omega;otherwise

(1)

PDFX&comma;0.5

&Gamma;0.5000000000&nu;&plus;0.5000000000&omega;&nu;&omega;0.5000000000&nu;0.50.5000000000&nu;1.&Gamma;0.5000000000&nu;&Gamma;0.5000000000&omega;1.&plus;0.5&nu;&omega;0.5000000000&nu;&plus;0.5000000000&omega;

(2)

MeanX

&lcub;undefined&omega;2&omega;2&plus;&omega;otherwise

(3)

VarianceX

&lcub;undefined&omega;42&omega;2&nu;&plus;&omega;2&nu;2&plus;&omega;24&plus;&omega;otherwise

(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]

 


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