Computes the complement of the cumulative distribution function of the F distribution.
cdfFc(x, df_n, df_d)¶
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.
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;
This procedure finds the complement of the F distribution cdf which equals
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.