logBeta¶
Evaluates the logarithm of the real beta function ln β(x, y).
Synopsis¶
logBeta (x, y)
Required Arguments¶
- float
x(Input) - Point at which the logarithm of the beta function is to be evaluated. It must be positive.
- float
y(Input) - Point at which the logarithm of the beta function is to be evaluated. It must be positive.
Return Value¶
The value of the logarithm of the beta function β(x, y).
Description¶
The beta function, β(x, y), is defined to be
\[\beta(x,y) = \frac{\mathit{\Gamma}(x)\mathit{\Gamma}(y)}{\mathit{\Gamma}(x+y)} =
\int_0^1 t^{x-1} (1-t)^{y-1} dt\]
and logBeta returns ln β(x, y).
The logarithm of the beta function requires that x > 0 and y > 0. It can overflow for very large arguments.
Example¶
Evaluate the log of the beta function ln β(0.5, 0.2).
from __future__ import print_function
from pyimsl.stat.logBeta import logBeta
x = 0.5
y = 0.2
ans = logBeta(x, y)
print("log beta(%f,%f) = %f\n" % (x, y, ans))
Output¶
log beta(0.500000,0.200000) = 1.835562
Warning Errors¶
IMSLS_X_IS_TOO_CLOSE_TO_NEG_1 |
The result is accurate to less
than one precision because the
expression −x/(x +
y) is too close to −1. |