# cdfFc¶

## Purpose¶

Computes the complement of the cumulative distribution function of the F distribution.

## Format¶

p = cdfFc(x, df_n, df_d)
Parameters: x (NxK matrix) – Values at which to evaluate the complement of the F distribution cdf. $$x > 0$$. df_n (LxM matrix) – ExE conformable with x. Degrees of freedom of numerator, $$df_n > 0$$. df_d (PxQ matrix) – ExE conformable with x and df_n. Degrees of freedom of denominator, $$df_d > 0$$. p (matrix, max(N,L,P) by max(K,M,Q)) – Each element in p is the complement of the F distribution cdf value evaluated at the corresponding element in x.

## Examples¶

cdffc() can be used to calculate a p-value from an F-statistic.

/*
** Computing the parameters
*/
// Number of observations
n_obs = 100;

// Number of variables
n_vars = 5;

df_n = n_vars;
df_d = n_obs - n_vars - 1;

// Value to calculate p_value at
f_stat = 2.4;

// Call cdfFc
p_value = cdfFc(f_stat, df_n, df_d);
print p_value;


will return:

0.042803132


## Remarks¶

This procedure finds the complement of the F distribution cdf which equals

$1 - G(x, df_n, df_d)$

where G is the F cdf with df_n and df_d degrees of freedom. Thus, to get the F cdf, use:

1 - cdfFc(x, df_n, df_d);


The complement of the cdf is computed because this is what is most commonly needed in statistical applications, and because it can be computed with fewer problems of roundoff error.

A -1 is returned for those elements with invalid inputs.

Functions cdfBeta(), cdfChic(), cdfN(), cdfNc(), cdfTc(), gamma()