boostmath (version 1.0.0)

beta_functions: Beta Functions

Description

Functions to compute the Euler beta function, normalised incomplete beta function, and their complements, as well as their inverses and derivatives.

Usage

beta_boost(a, b, x = NULL)
ibeta(a, b, x)
ibetac(a, b, x)
betac(a, b, x)
ibeta_inv(a, b, p)
ibetac_inv(a, b, q)
ibeta_inva(b, x, p)
ibetac_inva(b, x, q)
ibeta_invb(a, x, p)
ibetac_invb(a, x, q)
ibeta_derivative(a, b, x)

Value

A single numeric value with the computed beta function, normalised incomplete beta function, or their complements, depending on the function called.

Arguments

a

First parameter of the beta function

b

Second parameter of the beta function

x

Upper limit of integration (0 <= x <= 1)

p

Probability value (0 <= p <= 1)

q

Probability value (0 <= q <= 1)

See Also

Boost Documentation for more details on the mathematical background.

Examples

if (FALSE) {
# Euler beta function B(2, 3)
beta_boost(2, 3)
# Normalised incomplete beta function I_x(2, 3) for x = 0.5
ibeta(2, 3, 0.5)
# Normalised complement of the incomplete beta function 1 - I_x(2, 3) for x = 0.5
ibetac(2, 3, 0.5)
# Full incomplete beta function B_x(2, 3) for x = 0.5
beta_boost(2, 3, 0.5)
# Full complement of the incomplete beta function 1 - B_x(2, 3) for x = 0.5
betac(2, 3, 0.5)
# Inverse of the normalised incomplete beta function I_x(2, 3) = 0.5
ibeta_inv(2, 3, 0.5)
# Inverse of the normalised complement of the incomplete beta function I_x(2, 3) = 0.5
ibetac_inv(2, 3, 0.5)
# Inverse of the normalised complement of the incomplete beta function I_x(a, b)
# with respect to a for x = 0.5 and q = 0.5
ibetac_inva(3, 0.5, 0.5)
# Inverse of the normalised incomplete beta function I_x(a, b)
# with respect to b for x = 0.5 and p = 0.5
ibeta_invb(0.8, 0.5, 0.5)
# Inverse of the normalised complement of the incomplete beta function I_x(a, b)
# with respect to b for x = 0.5 and q = 0.5
ibetac_invb(2, 0.5, 0.5)
# Derivative of the incomplete beta function with respect to x for a = 2, b = 3, x = 0.5
ibeta_derivative(2, 3, 0.5)
}