betaInverseCdf¶

Evaluates the inverse of the beta distribution function.

Synopsis¶

betaInverseCdf (p, pin, qin)

Required Arguments¶

float p (Input): Probability for which the inverse of the beta distribution function is to be evaluated. Argument p must be in the open interval (0.0, 1.0).
float pin (Input): First beta distribution parameter. Argument pin must be positive.
float qin (Input): Second beta distribution parameter. Argument qin must be positive.

Return Value¶

Function betaInverseCdf returns the inverse distribution function of a beta random variable with parameters pin and qin.

Description¶

With P = p, p = pin, and q = qin, the betaInverseCdf returns x such that

\[P = \frac{\mathit{\Gamma}(p+q)}{\mathit{\Gamma}(p)\mathit{\Gamma}(q)} \int_0^x t^{p-1} (1-t)^{q-1} dt\]

where Γ (⋅) is the gamma function. In other words:

\[F^{-1}(P|pin,qin) = x\]

The probability that the random variable takes a value less than or equal to x is P.

Example¶

Suppose X is a beta random variable with parameters 12 and 12 (X has a symmetric distribution). In this example, we find the value x such that the probability that X is less than or equal to x is 0.9.

from __future__ import print_function
from numpy import *
from pyimsl.stat.betaInverseCdf import betaInverseCdf

pin = 12.0
qin = 12.0
p = 0.9
x = betaInverseCdf(p, pin, qin)
print(" X is less than %6.4f with probability 0.9." % x)

Output¶

 X is less than 0.6299 with probability 0.9.