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Student[Statistics]

  

StudentTRandomVariable

  

Student-t random variable

 

Calling Sequence

Parameters

Description

Examples

References

Compatibility

Calling Sequence

StudentTRandomVariable(nu)

Parameters

nu

-

degrees of freedom

Description

• 

The Student-t distribution is a continuous probability random variable with probability density function given by:

ft=Γν2+12πνΓν21+t2νν2+12

  

subject to the following conditions:

0<ν

• 

The StudentT variate is related to the Normal variate and the ChiSquare variate by the formula StudentT(nu) ~ Normal(0,1)/sqrt(ChiSquare(nu)/nu)

• 

The StudentT variate with degrees of freedom 1 is related to the standard Cauchy variate by StudentT(1) ~ Cauchy(0,1).

Examples

withStudentStatistics&colon;

XStudentTRandomVariable&nu;&colon;

PDFX&comma;u

Γν2+12πνΓν21+u2νν2+12

(1)

PDFX&comma;0.5

0.5641895835Γ0.5000000000ν+0.5000000000νΓ0.5000000000ν1.+0.25ν0.5000000000ν+0.5000000000

(2)

MeanX

undefinedν10otherwise

(3)

VarianceX

undefinedν2ν2+νotherwise

(4)

YStudentTRandomVariable5&colon;

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

CDFY&comma;x

12+8xhypergeom12&comma;3&comma;32&comma;x25515π

(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][StudentTRandomVariable] command was introduced in Maple 18.

• 

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

See Also

Statistics[Distributions][StudentT]

Student

Student[Statistics]

Student[Statistics][RandomVariable]