cdfFncInv

Purpose

Computes the quantile or inverse of noncentral F cumulative distribution function.

Format

x = cdfFncInv(p, df_n, df_d, nonc)
Parameters:
  • p (NxK matrix, Nx1 vector or scalar) – Probabilities at which to compute the inverse of the noncentral F cumulative distribution function. \(0 \lt p \lt 1\).
  • df_n (ExE conformable with p) – The degrees of freedom numerator. \(df_n > 0\).
  • df_d (ExE conformable with p) – The degrees of freedom denominator. \(df_d > 0\).
  • nonc (ExE conformable with p) – The noncentrality parameter. Note: This is the square root of the noncentrality parameter that sometimes goes under the symbol \(\lambda\). \(nonc > 0\).
Returns:

x (NxK matrix, Nx1 vector or scalar) – each value of x is the value such that the noncentral F cumulative distribution function with df_n, df_d, and nonc evaluated at x is equal to the corresponding value of p.

Examples

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

// Number of variables
n_vars = 5;

// Degrees of freedom
df_n = n_vars;
df_d = n_obs - n_vars - 1;

// Probabilities
p = {0.1, 0.25, 0.5, 0.75, 0.95};

// Non-centralty parameter
nonc = 2;

x = cdfFncInv(p, df_n, df_d, nonc);
print x;

After running the above code,

0.6483
1.0416
1.6350
2.4132
3.9044

Remarks

For invalid inputs, cdfFncInv() will return a scalar error code which, when its value is assessed by function scalerr(), corresponds to the invalid input. If the first input is out of range, scalerr() will return a 1; if the second is out of range, scalerr() will return a 2; etc.