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BetaDistribution

BetaDistribution[Alpha, Beta]
represents a continuous beta distribution with shape parameters Alpha and Beta.
  • The probability density for value x in a beta distribution is proportional to x^(alpha-1)(1-x)^(beta-1)for 0<x<1, and is zero for x<0 or x>1. »
EXAMPLESCLOSE ALL
Basic Examples   (2)
The mean and variance of a beta distribution:
The probability density function depends on the beta function:
The mean and variance of a beta distribution:
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The probability density function depends on the beta function:
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Scope   (4)
Generate a set of pseudorandom numbers that are beta distributed:
Properties based on higher-order moments:
Third moment of a beta distribution:
The 0.75 quantile of a beta distribution with Alpha=5 and Beta=2:
Applications   (2)
Plot the cumulative distribution function of the random variable:
A contour plot as both x and Beta are varied:
Properties & Relations   (3)
The probability density function integrates to unity:
Moments can be obtained from the characteristic function:
BetaDistribution[1, 1] is equivalent to UniformDistribution[{0, 1}]:
Possible Issues   (2)
BetaDistribution is not defined when either Alpha or Beta is not a positive real number:
Substitution of invalid parameters into symbolic outputs gives results that are not meaningful:
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