1: $p$ – double scalar: $p$ , the lower tail probability from the required $χ^{2}$ -distribution.

Constraint: $0.0 \leq p < 1.0$ .
2: $df$ – double scalar: $ν$ , the degrees of freedom of the $χ^{2}$ -distribution.

Constraint: $df > 0.0$ .

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_chisq (g01fc) 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

5

on exit, then nag_stat_inv_cdf_chisq (g01fc) 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,

df \leq 0.0

$ifail = 3$: p is too close to $0$ or $1$ for the result to be calculated.

W $ifail = 4$: The solution has failed to converge. The result should be a reasonable approximation.

$ifail = 5$: The series used to calculate the gamma function has failed to converge. This is an unlikely error exit.

$ifail = - 99$: 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 results should be accurate to five significant digits for most argument values. Some accuracy is lost for

p

close to

0.0

Further Comments

For higher accuracy the relationship described in Description may be used and a direct call to nag_stat_inv_cdf_gamma (g01ff) made.

Example

This example reads lower tail probabilities for several

χ^{2}

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

Open in the MATLAB editor: g01fc_example

function g01fc_example


fprintf('g01fc example results\n\n');

p    = [ 0.01;   0.428;   0.869];
df   = [20.00;   7.500;  45.000];

fprintf('      p      df       x\n');
for j = 1:numel(p);

  [x, ifail] = g01fc( ...
                      p(j) , df(j));

  fprintf('%9.3f%8.3f%8.3f\n', p(j), df(j), x);
end

g01fc example results

      p      df       x
    0.010  20.000   8.260
    0.428   7.500   6.201
    0.869  45.000  55.738

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

Chapter Contents

Chapter Introduction

NAG Toolbox