betaIncomplete¶
Evaluates the real regularized incomplete beta function.
Synopsis¶
betaIncomplete (x, a, b)
Required Arguments¶
- float
x
(Input) - Argument at which the regularized incomplete beta function is to be evaluated.
- float
a
(Input) - First shape parameter.
- float
b
(Input) - Second shape parameter.
Return Value¶
The value of the regularized incomplete beta function.
Description¶
The regularized incomplete beta function \(I_x(a,b)\) is defined
where
is the incomplete beta function,
is the (complete) beta function, and \(\mathit{\Gamma} (a)\) is the gamma function.
The regularized incomplete beta function betaIncomplete
(x
, a
,
b
) is identical to the beta probability distribution function
betaCdf (x
, a
, b
) which represents the
probability that a beta random variable X with shape parameters a and
b takes on a value less than or equal to x. The regularized incomplete
beta function requires that 0 ≤ x ≤ 1, a > 0, and b > 0 and it
underflows for sufficiently small x and large a. This underflow is not
reported as an error. Instead, the value zero is returned.
Example¶
Suppose X is a beta random variable with shape parameters \(a=b=12\) (X has a symmetric distribution). This example finds the probability that X is less than 0.6 and the probability that X is between 0.5 and 0.6. (Since X is a symmetric beta random variable, the probability that it is less than 0.5 is 0.5.)
from __future__ import print_function
from pyimsl.stat.betaIncomplete import betaIncomplete
x = 0.61
a = 2.2
b = 3.7
ans = betaIncomplete(x, a, b)
print("beta incomplete = ", ans)
Output¶
beta incomplete = 0.8821718196830987