gives the regularized incomplete beta function .
- Mathematical function, suitable for both symbolic and numerical manipulation.
- For nonsingular cases, .
- BetaRegularized[z0,z1,a,b] gives the generalized regularized incomplete beta function defined in nonsingular cases as Beta[z0,z1,a,b]/Beta[a,b].
- Note that the arguments in BetaRegularized are arranged differently from those in GammaRegularized.
- For certain special arguments, BetaRegularized automatically evaluates to exact values.
- BetaRegularized can be evaluated to arbitrary numerical precision.
- BetaRegularized automatically threads over lists.
Examplesopen allclose all
Basic Examples (6)
Asymptotic expansion at Infinity:
Numerical Evaluation (4)
Specific Values (4)
Plot the BetaRegularized function for various parameters:
Function Properties (9)
Compute the indefinite integral using Integrate:
Series Expansions (5)
Function Identities and Simplifications (3)
BetaRegularized may reduce to a simpler form:
Generalizations & Extensions (8)
Ordinary Regularized Incomplete Beta Function (5)
Plot of the absolute value of BetaRegularized in the complex plane:
CDF of the Student t distribution:
Plot the CDF for various parameters:
Properties & Relations (3)
Possible Issues (3)
Large arguments can give results too large to be computed explicitly:
Machine‐number inputs can give high‐precision results:
Regularized beta functions are typically not generated by FullSimplify:
Wolfram Research (1991), BetaRegularized, Wolfram Language function, https://reference.wolfram.com/language/ref/BetaRegularized.html.
Wolfram Language. 1991. "BetaRegularized." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/BetaRegularized.html.
Wolfram Language. (1991). BetaRegularized. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/BetaRegularized.html