tInverseCdf¶

Evaluates the inverse of the Student’s t distribution function.

Synopsis¶

tInverseCdf (p, df)

Required Arguments¶

float p (Input): Probability for which the inverse of the Student’s t distribution function is to be evaluated. Argument p must be in the open interval (0.0, 1.0).
float df (Input): Degrees of freedom. Argument df must be greater than or equal to 1.0.

Return Value¶

The inverse of the Student’s t distribution function evaluated at p. The probability that a Student’s t random variable takes a value less than or equal to tInverseCdf is p.

Description¶

The function tInverseCdf evaluates the inverse distribution function of a Student’s t random variable with \(\nu=df\) degrees of freedom. If ν equals 1 or 2, the inverse can be obtained in closed form. If ν is between 1 and 2, the relationship of a t to a beta random variable is exploited, and the inverse of the beta distribution is used to evaluate the inverse; otherwise, the algorithm of Hill (1970) is used. For small values of ν greater than 2, Hill’s algorithm inverts an integrated expansion in \(1/(1+t^2/\nu)\) of the t density. For larger values, an asymptotic inverse Cornish-Fisher type expansion about normal deviates is used.

Example¶

This example finds the 0.05 critical value for a two-sided t test with six degrees of freedom.

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

df = 6.0
p = 0.975

t = tInverseCdf(p, df)
print("The two-sided t(6) 0.05 critical value is %6.3f" % (t))

Output¶

The two-sided t(6) 0.05 critical value is  2.447

Informational Errors¶

IMSL_OVERFLOW Function tInverseCdf is set to machine infinity since overflow would occur upon modifying the inverse value for the F distribution with the result obtained from the inverse beta distribution.