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Statistics[Distributions][Beta] - beta distribution
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Calling Sequence
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'Beta'(nu, omega)
BetaDistribution(nu, omega)
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Parameters
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nu
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first shape parameter
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omega
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second shape parameter
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Description
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The beta distribution is a continuous probability distribution with probability density function given by:
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subject to the following conditions:
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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)).
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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  looks like a capital letter  , but the two are different in Maple.
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Examples
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The following is invalid.
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Alternatives are:
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and
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![PIECEWISE([0, u < 0], [u^(-1+nu)*(1-u)^(-1+omega)/Beta(nu, omega), u < 1], [0, otherwise])](/support/helpjp/helpview.aspx?si=4642/file06569/math134.png)
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References
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Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.
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Johnson, Norman L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.
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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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