1: $p$ – double scalar: $p$ , the probability from the required Student's $t$ -distribution as defined by tail.

Constraint: $0.0 < p < 1.0$ .
2: $df$ – double scalar: $ν$ , the degrees of freedom of the Student's $t$ -distribution.

Constraint: $df \geq 1.0$ .

Optional Input Parameters

1: $tail$ – string (length ≥ 1)

Default:

'L'

Indicates which tail the supplied probability represents.

$tail ='U'$: The upper tail probability, i.e., $P (T \geq t_{p} : ν)$ .
$tail ='L'$: The lower tail probability, i.e., $P (T \leq t_{p} : ν)$ .
$tail ='S'$: The two tail (significance level) probability, i.e., $P (T \geq |t_{p}| : ν) + P (T \leq - |t_{p}| : ν)$ .
$tail ='C'$: The two tail (confidence interval) probability, i.e., $P (T \leq |t_{p}| : ν) - P (T \leq - |t_{p}| : ν)$ .

Constraint:

tail ='U'

'L'

'S'

'C'

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_students_t (g01fb) 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_inv_cdf_students_t (g01fb) returns zero.

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,

tail \neq'U'

'S'

'C'

'L'

$ifail = 2$

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

$ifail = 3$

On entry,

df < 1.0

W $ifail = 5$: Convergence in the calculation of the inverse beta value was not achieved. However, the result should be a reasonable approximation to the correct value.

$ifail = - 99$: 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. The error behaviour for various argument values is discussed in Hill (1970).

Further Comments

The value

t_{p}

may be calculated by using the transformation described in Description and using nag_stat_inv_cdf_beta (g01fe). This function allows you to set the required accuracy.

Example

This example reads the probability, the tail that probability represents and the degrees of freedom for a number of Student's

t

-distributions and computes the corresponding deviates.

Open in the MATLAB editor: g01fb_example

function g01fb_example


fprintf('g01fb example results\n\n');

p    = [ 0.01;          0.01;        0.99];
df   = [20;             7.5;        45.00];
tail = {'Significance'; 'Lower'; 'Confidence' };

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

  [x, ifail] = g01fb( ...
                      p(j) , df(j), 'tail', tail{j});

  fprintf('%9.3f%8.3f%4s%12.3f\n', p(j), df(j), tail{j}(1), x);
end

g01fb example results

      p      df    tail      x
    0.010  20.000   S       2.845
    0.010   7.500   L      -2.943
    0.990  45.000   C       2.690

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

Chapter Contents

Chapter Introduction

NAG Toolbox