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FRatioRandomVariable

  

f-ratio random variable

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

FRatioRandomVariable(nu, omega)

Parameters

nu

-

first degrees of freedom parameter

omega

-

second degrees of freedom parameter

Description

• 

The f-ratio random variable is a continuous probability random variable 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))

Examples

withStudent&lsqb;Statistics&rsqb;&colon;

XFRatioRandomVariable&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)

YFRatioRandomVariable7&comma;8&colon;

PDFY&comma;x&comma;output&equals;plot

CDFY&comma;x

&lcub;0x043904x7&sol;28&plus;7x343x3&plus;2548x2&plus;8008x&plus;137287216&plus;14x15&sol;20<x

(5)

CDFY&comma;3&comma;output&equals;plot

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.

Compatibility

• 

The Student[Statistics][FRatioRandomVariable] command was introduced in Maple 18.

• 

For more information on Maple 18 changes, see Updates in Maple 18.

See Also

Statistics[Distributions][FRatio]

Student

Student[Statistics]

Student[Statistics][RandomVariable]

 


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