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Student[Statistics][BetaRandomVariable] - beta random variable

Calling Sequence

BetaRandomVariable(nu, omega)

Parameters

nu

-

first shape parameter

omega

-

second shape parameter

Description

• 

The beta distribution is a continuous probability distribution with probability density function given by:

ft=0t<0t1+ν1t1+ωΒν&comma;ωt<10otherwise

  

subject to the following conditions:

0<ν,0<ω

• 

The beta random variable is related to the independent Gamma variates Gamma(1,nu) and Gamma(1,omega) by the formula Beta(nu,omega) ~ Gamma(1,nu)/(Gamma(1,nu)+Gamma(1,omega)).

Examples

withStudent&lsqb;Statistics&rsqb;&colon;

X:=BetaRandomVariable&nu;&comma;&omega;&colon;

PDFX&comma;u

&lcub;0u<0u&nu;11u&omega;1&Beta;&nu;&comma;&omega;u<10otherwise

(1)

PDFX&comma;0.5

0.5&nu;1.0.51.&plus;&omega;&Beta;&nu;&comma;&omega;

(2)

MeanX

&nu;&nu;&plus;&omega;

(3)

VarianceX

&nu;&omega;&nu;&plus;&omega;2&nu;&plus;&omega;&plus;1

(4)

Y:=BetaRandomVariable4&comma;7&colon;

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

CDFY&comma;x

&lcub;0x<0210x4hypergeom6&comma;4&comma;5&comma;xx<11otherwise

(5)

CDFY&comma;0.5&comma;output&equals;plot

See Also

Statistics[Distributions][Beta], Student, Student[Statistics], Student[Statistics][RandomVariable]

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.


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