1: $x$ – double scalar: $x$ , the value of the $χ^{2}$ variate with $ν$ degrees of freedom.

Constraint: $x \geq 0.0$ .
2: $df$ – double scalar: $ν$ , the degrees of freedom of the $χ^{2}$ -distribution.

Constraint: $df > 0.0$ .

Optional Input Parameters

1: $tail$ – string (length ≥ 1)

Default:

'L'

Indicates whether the upper or lower tail probability is required.

$tail ='L'$: The lower tail probability is returned, i.e., $P (X \leq x : ν)$ .
$tail ='U'$: The upper tail probability is returned, i.e., $P (X \geq x : ν)$ .

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_chisq (g01ec) 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_chisq (g01ec) returns

0.0

$ifail = 1$

On entry,

tail \neq'L'

'U'

$ifail = 2$

On entry,

x < 0.0

$ifail = 3$

On entry,

df \leq 0.0

$ifail = 4$: The solution has failed to converge while calculating the gamma variate. The result returned should represent an approximation to the 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

A relative accuracy of five significant figures is obtained in most cases.

Further Comments

For higher accuracy the transformation described in Description may be used with a direct call to nag_specfun_gamma_incomplete (s14ba).

Example

Values from various

χ^{2}

-distributions are read, the lower tail probabilities calculated, and all these values printed out, until the end of data is reached.

Open in the MATLAB editor: g01ec_example

function g01ec_example


fprintf('g01ec example results\n\n');

% Lower tail probabilities for Chi^2 distribution
x  = [ 8.26; 6.2; 55.76];
df = [20.00; 7.5; 45.00];
tail = {'Lower'; 'Lower'; 'Lower';};

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

  [p, ifail] = g01ec( ...
                      x(j), df(j), 'tail', tail{j});

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

g01ec example results

  Tail    x      df    probability
   L   8.260    20.0      0.0100
   L   6.200     7.5      0.4279
   L  55.760    45.0      0.8694

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

Chapter Contents

Chapter Introduction

NAG Toolbox