Statistics[Distributions] - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Statistics and Data Analysis : Statistics Package : Distributions : Statistics/Distributions/FRatio

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

0u<0Γν2+ω2νων2uν21Γν2Γω21+νuων2+ω2otherwise

(1)

PDFX&comma;0.5

Γ0.5000000000ν+0.5000000000ωνω0.5000000000ν0.50.5000000000ν1.Γ0.5000000000νΓ0.5000000000ω1.+0.5νω0.5000000000ν+0.5000000000ω

(2)

MeanX

undefinedω2ω2+ωotherwise

(3)

VarianceX

undefinedω42ω2ν+ω2ν2+ω24+ωotherwise

(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]