IncBeta {HypergeoMat}

Incomplete Beta function of a matrix argument

Description

Evaluates the incomplete Beta function of a matrix argument.

Usage

IncBeta(m, a, b, x)

Arguments

m

truncation weight of the summation, a positive integer

a, b

real or complex parameters with Re(a)>(p-1)/2 and Re(b)>(p-1)/2, where p is the dimension (the order of the matrix)

x

either a real positive symmetric matrix or a complex positive Hermitian matrix "smaller" than the identity matrix (i.e. I-x is positive), or a numeric or complex vector, the eigenvalues of the matrix

Value

A real or a complex number.

Note

The eigenvalues of a real symmetric matrix or a complex Hermitian matrix are always real numbers, and moreover they are positive under the constraints on x. However we allow to input a numeric or complex vector x because the definition of the function makes sense for such a x.

References

A. K. Gupta and D. K. Nagar. Matrix variate distributions. Chapman and Hall, 1999.

Examples

# for a scalar x, this is the incomplete Beta function:
a <- 2; b <- 3
x <- 0.75
IncBeta(m = 15, a, b, x)
gsl::beta_inc(a, b, x)
pbeta(x, a, b)