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Statistics[Distributions]

  

Beta

  

beta distribution

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

'Beta'(nu, omega)

BetaDistribution(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 distribution 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)).

• 

Note that the Beta(a, b) returns the value of the Beta function with parameters a and b, so in order to define a Beta random variable one should use the unevaluated name 'Beta'. In 2D math notation, the capital letter Β looks like a capital letter B, but the two are different in Maple.

Examples

withStatistics&colon;

The following is invalid.

RandomVariable&Beta;1&comma;2

Error, (in Statistics:-Distribution) invalid input: too many and/or wrong type of arguments passed to Statistics:-Distributions:-DataStructure:-NewDistribution; first unused argument is 1/2

Alternatives are:

RandomVariable&apos;&Beta;&apos;1&comma;2

_R

(1)

and

RandomVariableBetaDistribution1&comma;2

_R0

(2)

XRandomVariable&apos;&Beta;&apos;&nu;&comma;&omega;&colon;

PDFX&comma;u

&lcub;0u<0u1&plus;&nu;1u1&plus;&omega;&Beta;&nu;&comma;&omega;u<10otherwise

(3)

PDFX&comma;0.5

0.51.&plus;&nu;0.51.&plus;&omega;&Beta;&nu;&comma;&omega;

(4)

MeanX

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

(5)

VarianceX

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

(6)

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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