Student[Statistics]
BetaRandomVariable
beta random variable
Calling Sequence
Parameters
Description
Examples
References
Compatibility
BetaRandomVariable(nu, omega)
nu
-
first shape parameter
omega
second shape parameter
The beta distribution is a continuous probability distribution with probability density function given by:
ft=0t<0t−1+ν1−t−1+ωΒν,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)).
withStudentStatistics:
X≔BetaRandomVariableν,ω:
PDFX,u
0u<0u−1+ν1−u−1+ωΒν,ωu<10otherwise
PDFX,0.5
0.5−1.+ν0.5−1.+ωΒν,ω
MeanX
νν+ω
VarianceX
νων+ω2ν+ω+1
Y≔BetaRandomVariable4,7:
PDFY,x,output=plot
CDFY,x
0x<0210x4hypergeom−6,4,5,xx<11otherwise
CDFY,0.5,output=plot
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.
The Student[Statistics][BetaRandomVariable] command was introduced in Maple 18.
For more information on Maple 18 changes, see Updates in Maple 18.
See Also
Statistics[Distributions][Beta]
Student
Student[Statistics][RandomVariable]
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