betainc

Incomplete beta function

📝 Syntax

• R = betainc(X, Z, W)

• R = betainc(X, Z, W, tail)

📥 Input argument

• X - a real single or real double matrix. It must be in the closed interval [0, 1].

• Z - a real single or real double matrix. It must be nonnegative.

• W - a real single or real double matrix. It must be nonnegative.

• tail - a string 'upper' or 'lower' (default).

📤 Output argument

• R - result of betainc function.

📄 Description

betainc computes the incomplete beta function (regularized).

The incomplete beta function is defined as: $I_x(a,b) = \frac{B(x; a,b)}{B(a,b)} = \frac{1}{B(a,b)} \int_0^x t^{a-1} (1-t)^{b-1} \, dt$

where $B(a,b) = \int_0^1 t^{a-1} (1-t)^{b-1} \, dt$

is the complete beta function, and: $B(a,b) = \frac{\Gamma(a)\Gamma(b)}{\Gamma(a+b)}$

The function is normalized so that $I_1(a,b) = 1$ .

All arrays must be the same size or any of them can be scalar.

💡 Example

R = betainc(0.5, 1:10, 3)

🔗 See also

gamma.

🕔 History

Version	📄 Description
1.0.0	initial version