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 evaluates the inverse distribution function of a beta random variable with parameters pin and qin.

Description

With P = p, p = pin, and q = qin, function 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. 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.) This example finds the value x such that the probability that Xx is 0.9.

from __future__ import print_function
from numpy import *
from pyimsl.math.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.