Difference between revisions of "BetaFn"

Latest revision as of 21:23, 5 February 2016

BetaFn(a, b)

The complete beta function, defined as:

[math]\displaystyle{ BetaFn(a,b) = \int_0^1 x^{a-1} (1-x)^{b-1} dx }[/math]

The following relationship exists between the BetaFn and the GammaFn:

BetaFn(a,b) = GammaFn(a) * GammaFn(b) / GammaFn(a+b)

Numeric considerations

For very large values of a and b, the result underflow, so that you might find it better to use Ln(BetaFn(a,b)). However, when computing the log-beta function, you should compute it using:

LGamma(a) + LGamma(b) - LGamma(a+b)

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 [[category:Analytic Distribution Functions]]
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+== BetaFn(a, b) ==
+The complete [[beta]] function, defined as:
+:<math>BetaFn(a,b) = \int_0^1 x^{a-1} (1-x)^{b-1} dx</math>
+The following relationship exists between the [[BetaFn]] and the [[GammaFn]]:
+:[[BetaFn]](a,b) = [[GammaFn]](a) * [[GammaFn]](b) / [[GammaFn]](a+b)
+== Numeric considerations ==
+For very large values of <code>a</code> and <code>b</code>, the result underflow, so that you might find it better to use <code>[[Ln]]([[BetaFn]](a,b))</code>. However, when computing the log-beta function, you should compute it using:
+:<code>[[LGamma]](a) + [[LGamma]](b) - [[LGamma]](a+b)</code>
+== See Also ==
+* [[Beta]]
+* [[BetaI]] : The incomplete beta function
+* [[GammaFn]] : The complete gamma function
+* [[Parametric continuous distributions]]
+* [[Distribution Densities Library]]