1: $f$ – double scalar: $f$ , the value of the $F$ variate.

Constraint: $f \geq 0.0$ .
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

1: $tail$ – string (length ≥ 1)

Default:

'L'

Indicates whether an upper or lower tail probability is required.

$tail ='L'$: The lower tail probability is returned, i.e., $P (F \leq f : ν_{1}, ν_{2})$ .
$tail ='U'$: The upper tail probability is returned, i.e., $P (F \geq f : ν_{1}, ν_{2})$ .

Constraint:

tail ='L'

'U'

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_prob_f (g01ed) may return useful information for one or more of the following detected errors or warnings.

Errors or warnings detected by the function:

ifail = 1

2

3

on exit, then nag_stat_prob_f (g01ed) returns

0.0

$ifail = 1$

On entry,

tail \neq'L'

'U'

$ifail = 2$

On entry,

f < 0.0

$ifail = 3$

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

$ifail = 4$: f is too far out into the tails for the probability to be evaluated exactly. The result tends to approach $1.0$ if $f$ is large, or $0.0$ if $f$ is small. The result returned is a good approximation to the required solution.

$ifail = - 99$: 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_prob_beta (g01ee) can be used along with the transformations given in Description.

Example

This example reads values from, and degrees of freedom for, a number of

F

-distributions and computes the associated lower tail probabilities.

Open in the MATLAB editor: g01ed_example

function g01ed_example


fprintf('g01ed example results\n\n');

% Lower tail probabilities for F distribution
f   = [ 5.5; 39.9;  2.50];
df1 = [ 1.5;  1.0; 20.25]; 
df2 = [25.5;  1.0;  1.00];
tail = {'Lower'; 'Lower'; 'Lower';};

fprintf('  Tail    F      df1     df2    probability\n');
for j = 1:numel(f);

  [p, ifail] = g01ed( ...
                      f(j), df1(j), df2(j), 'tail', tail{j});

  fprintf('%4s%8.3f%8.1f%8.1f%12.4f\n',tail{j}(1), f(j), df1(j), df2(j), p);
end

g01ed example results

  Tail    F      df1     df2    probability
   L   5.500     1.5    25.5      0.9837
   L  39.900     1.0     1.0      0.9000
   L   2.500    20.2     1.0      0.5342

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

Chapter Contents

Chapter Introduction

NAG Toolbox