$tail = Nag_UpperTail$: The upper tail probability, i.e., $P (T \geq t_{p} : ν)$ .
$tail = Nag_LowerTail$: The lower tail probability, i.e., $P (T \leq t_{p} : ν)$ .
$tail = Nag_TwoTailSignif$: The two tail (significance level) probability, i.e., $P (T \geq |t_{p}| : ν) + P (T \leq - |t_{p}| : ν)$ .
$tail = Nag_TwoTailConfid$: The two tail (confidence interval) probability, i.e., $P (T \leq |t_{p}| : ν) - P (T \leq - |t_{p}| : ν)$ .

Constraint:

tail = Nag_UpperTail

Nag_LowerTail

Nag_TwoTailSignif

Nag_TwoTailConfid

2: $p$ – double Input

On entry:

p

, the probability from the required Student's

t

-distribution as defined by tail.

Constraint:

0.0 < p < 1.0

3: $df$ – double Input

On entry:

ν

, the degrees of freedom of the Student's

t

-distribution.

Constraint:

df \geq 1.0

4: $fail$ – NagError * Input/Output

The NAG error argument (see Section 7 in the Introduction to the NAG Library CL Interface).

6 Error Indicators and Warnings

On any of the error conditions listed below except $fail . code =$ NE_SOL_NOT_CONV g01fbc returns $0.0$ .
NE_ALLOC_FAIL: Dynamic memory allocation failed.
See Section 3.1.2 in the Introduction to the NAG Library CL Interface for further information.
NE_BAD_PARAM: On entry, argument $〈value〉$ had an illegal value.
NE_INTERNAL_ERROR: An internal error has occurred in this function. Check the function call and any array sizes. If the call is correct then please contact NAG for assistance.
See Section 7.5 in the Introduction to the NAG Library CL Interface for further information.
NE_NO_LICENCE: Your licence key may have expired or may not have been installed correctly.
See Section 8 in the Introduction to the NAG Library CL Interface for further information.
NE_REAL_ARG_GE: On entry, $p = 〈value〉$ .
Constraint: $p < 1.0$ .
NE_REAL_ARG_LE: On entry, $p = 〈value〉$ .
Constraint: $p > 0.0$ .
NE_REAL_ARG_LT: On entry, $df = 〈value〉$ .
Constraint: $df \geq 1.0$ .
NE_SOL_NOT_CONV: The solution has failed to converge. However, the result should be a reasonable approximation.

7 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).

8 Parallelism and Performance

g01fbc is not threaded in any implementation.

9 Further Comments

The value

t_{p}

may be calculated by using the transformation described in Section 3 and using g01fec. This function allows you to set the required accuracy.

9.1 Internal Changes

Internal changes have been made to this function as follows:

At Mark 27: The algorithm underlying this function has been altered to improve the accuracy in cases where $df < 3$ .

For details of all known issues which have been reported for the NAG Library please refer to the Known Issues.

10 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.

Interfaces: FL CL AD

NAG CL Interface Introduction

G01 (Stat) Chapter Contents

G01 (Stat) Chapter Introduction

g01fb: FL CL AD

NAG CL Interfaceg01fbc (inv_​cdf_​students_​t)

▸▿ Contents

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

6 Error Indicators and Warnings

7 Accuracy

8 Parallelism and Performance

9 Further Comments

9.1 Internal Changes

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results

NAG CL Interface
g01fbc (inv_cdf_students_t)