fInverseCdf¶
Evaluates the inverse of the F distribution function.
Synopsis¶
fInverseCdf (p, dfNumerator, dfDenominator)
Required Arguments¶
- float
p
(Input) - Probability for which the inverse of the F distribution function is to
be evaluated. The argument
p
must be in the open interval (0.0, 1.0). - float
dfNumerator
(Input) - Numerator degrees of freedom. Argument
dfNumerator
must be positive. - float
df_denominato
r (Input) - Denominator degrees of freedom. Argument
dfDenominator
must be positive.
Return Value¶
The value of the inverse of the F distribution function evaluated at
p
. The probability that an F random variable takes a value less than
or equal to fInverseCdf
is p
.
Description¶
The function fInverseCdf
evaluates the inverse distribution function of a
Snedecor’s F random variable with \(\nu_1\) = dfNumerator
numerator
degrees of freedom and \(\nu_2\) = dfDenominator
denominator degrees
of freedom. The function is evaluated by making a transformation to a beta
random variable and then by evaluating the inverse of an incomplete beta
function. If X is an F variate with \(\nu_1\) and \(\nu_2\)
degrees of freedom and \(Y=(\nu_1,X)/(\nu_2+\nu_1 X)\), then Y is a
beta variate with parameters \(p=\nu_1/2\) and \(q=\nu_2/2\). If
\(P\leq 0.5\), fInverseCdf
uses this relationship directly;
otherwise, it also uses a relationship between F random variables that can
be expressed as follows:
Example¶
In this example, the 99-th percentage point is calculated for an F random variable with seven degrees of freedom. The same calculation is made for a similar variable with one degree of freedom.
from __future__ import print_function
from numpy import *
from pyimsl.math.fInverseCdf import fInverseCdf
df_denominator = 1.0
df_numerator = 7.0
p = 0.99
f = fInverseCdf(p, df_numerator, df_denominator)
print("The F(7,1) 0.01 critical value is %6.3f" % (f))
Output¶
The F(7,1) 0.01 critical value is 5928.356
Fatal Errors¶
INVERSE_OVERFLOW |
Function fInverseCdf 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. |