BetaRegularized

The regularized incomplete beta function , the CDF of the Beta(a, b) distribution and a bridge to the binomial CDF.

Wolfram LanguageBetaRegularized!↗

BetaRegularized(x, a, b)the regularized incomplete beta function .

Domain: Special functions

Details

• Normalized against Beta: is the incomplete beta integral at x, divided by , so and .
• Symmetry: .
• Ties to the binomial CDF: for , .
• By symmetry, for any a: a symmetric Beta(a, a) distribution has its median exactly at the midpoint.
• compute-engine leaves x outside symbolic rather than erroring or returning NaN.

Examples

See also: Beta, GammaRegularized, Binomial