NAG C Library Function Document

nag_deviates_students_t (g01fbc)

1

Purpose

2

Specification

3

Description

4

References

5

Arguments

1:    $\mathbf{tail}$ – Nag_TailProbabilityInput

On entry: indicates which tail the supplied probability represents.

$\mathbf{tail}=\mathrm{Nag\_UpperTail}$

The upper tail probability, i.e., $P\left(T\ge t_p:\nu \right)$.

$\mathbf{tail}=\mathrm{Nag\_LowerTail}$

The lower tail probability, i.e., $P\left(T\le t_p:\nu \right)$.

$\mathbf{tail}=\mathrm{Nag\_TwoTailSignif}$

The two tail (significance level) probability, i.e., $P\left(T\ge \left|t_p\right|:\nu \right)+P\left(T\le -\left|t_p\right|:\nu \right)$.

$\mathbf{tail}=\mathrm{Nag\_TwoTailConfid}$

The two tail (confidence interval) probability, i.e., $P\left(T\le \left|t_p\right|:\nu \right)-P\left(T\le -\left|t_p\right|:\nu \right)$.

Constraint: $\mathbf{tail}=\mathrm{Nag\_UpperTail}$, $\mathrm{Nag\_LowerTail}$, $\mathrm{Nag\_TwoTailSignif}$ or $\mathrm{Nag\_TwoTailConfid}$.

2:    $\mathbf{p}$ – doubleInput

On entry: $p$, the probability from the required Student's $t$-distribution as defined by tail.

Constraint: $0.0<\mathbf{p}<1.0$.

3:    $\mathbf{df}$ – doubleInput

On entry: $\nu$, the degrees of freedom of the Student's $t$-distribution.

Constraint: $\mathbf{df}\ge 1.0$.

4:    $\mathbf{fail}$ – NagError *Input/Output

The NAG error argument (see Section 3.7 in How to Use the NAG Library and its Documentation).

6

Error Indicators and Warnings

On any of the error conditions listed below except $\mathbf{fail}\mathbf{.}\mathbf{code}=$ NE_SOL_NOT_CONV nag_deviates_students_t (g01fbc) returns $0.0$.

NE_ALLOC_FAIL

Dynamic memory allocation failed.
See Section 2.3.1.2 in How to Use the NAG Library and its Documentation for further information.

NE_BAD_PARAM

On entry, argument $〈\mathit{\text{value}}〉$ 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 2.7.6 in How to Use the NAG Library and its Documentation for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 2.7.5 in How to Use the NAG Library and its Documentation for further information.

NE_REAL_ARG_GE

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}<1.0$.

NE_REAL_ARG_LE

On entry, $\mathbf{p}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{p}>0.0$.

NE_REAL_ARG_LT

On entry, $\mathbf{df}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{df}\ge 1.0$.

NE_SOL_NOT_CONV

The solution has failed to converge. However, the result should be a reasonable approximation.

7

Accuracy

8

Parallelism and Performance

9

Further Comments

10

Example

10.1

Program Text

Program Text (g01fbce.c)

10.2

Program Data

Program Data (g01fbce.d)

10.3

Program Results

Program Results (g01fbce.r)