1: $p$ – double scalar: $p$ , the lower tail probability from the required $F$ -distribution.

Constraint: $0.0 \leq p < 1.0$ .
2: $df1$ – double scalar: The degrees of freedom of the numerator variance, $ν_{1}$ .

Constraint: $df1 > 0.0$ .
3: $df2$ – double scalar: The degrees of freedom of the denominator variance, $ν_{2}$ .

Constraint: $df2 > 0.0$ .

Optional Input Parameters

None.

Output Parameters

1: $result$ – double scalar: The result of the function.
2: $ifail$ – int64int32nag_int scalar: $ifail = 0$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Note: nag_stat_inv_cdf_f (g01fd) may return useful information for one or more of the following detected errors or warnings.

Errors or warnings detected by the function:

If on exit

ifail = 1

2

4

, then nag_stat_inv_cdf_f (g01fd) returns

0.0

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

$ifail = 1$

On entry,	$p < 0.0$ ,
or	$p \geq 1.0$ .

$ifail = 2$

On entry,	$df1 \leq 0.0$ ,
or	$df2 \leq 0.0$ .

W $ifail = 3$: The solution has not converged. The result should still be a reasonable approximation to the solution. Alternatively, nag_stat_inv_cdf_beta (g01fe) can be used with a suitable setting of the argument tol.

$ifail = 4$: The value of p is too close to $0$ or $1$ for the value of $f_{p}$ to be computed. This will only occur when the large sample approximations are used.

$ifail = - 99$: An unexpected error has been triggered by this routine. Please contact NAG.

$ifail = - 399$: Your licence key may have expired or may not have been installed correctly.

$ifail = - 999$: Dynamic memory allocation failed.

Accuracy

The result should be accurate to five significant digits.

Further Comments

For higher accuracy nag_stat_inv_cdf_beta (g01fe) can be used along with the transformations given in Description.

Example

This example reads the lower tail probabilities for several

F

-distributions, and calculates and prints the corresponding deviates until the end of data is reached.

Open in the MATLAB editor: g01fd_example

function g01fd_example


fprintf('g01fd example results\n\n');

p   = [ 0.9837  0.9000   0.5342];
df1 = [10       1       20.25  ];
df2 = [25.5     1        1     ];
fp  = p;

fprintf('     p      df1     df2      f_p\n');
for j = 1:numel(p)
   [fp(j), ifail] = g01fd( ...
			   p(j), df1(j), df2(j));
end

fprintf('%8.3f%8.3f%8.3f%8.3f\n', [p; df1; df2; fp]);

g01fd example results

     p      df1     df2      f_p
   0.984  10.000  25.500   2.837
   0.900   1.000   1.000  39.863
   0.534  20.250   1.000   2.500

PDF version (NAG web site, 64-bit version, 64-bit version)

Chapter Contents

Chapter Introduction

NAG Toolbox