NAG Library Routine Document

G01SCF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     $\mathrm{LTAIL}$ – INTEGERInput

On entry: the length of the array TAIL.

Constraint: $\mathbf{LTAIL}>0$.

2:     $\mathrm{TAIL}\left(\mathbf{LTAIL}\right)$ – CHARACTER(1) arrayInput

On entry: indicates whether the lower or upper tail probabilities are required. For $j=\left(\left(\mathit{i}-1\right)\mathrm{ mod }\mathbf{LTAIL}\right)+1$, for $\mathit{i}=1,2,\dots ,\max \left(\mathbf{LTAIL},\mathbf{LX},\mathbf{LDF}\right)$:

$\mathbf{TAIL}\left(j\right)=\text{'L'}$

The lower tail probability is returned, i.e., $p_i=P\left(X_i\le x_i:{\nu }_i\right)$.

$\mathbf{TAIL}\left(j\right)=\text{'U'}$

The upper tail probability is returned, i.e., $p_i=P\left(X_i\ge x_i:{\nu }_i\right)$.

Constraint: $\mathbf{TAIL}\left(\mathit{j}\right)=\text{'L'}$ or $\text{'U'}$, for $\mathit{j}=1,2,\dots ,\mathbf{LTAIL}$.

3:     $\mathrm{LX}$ – INTEGERInput

On entry: the length of the array X.

Constraint: $\mathbf{LX}>0$.

4:     $\mathrm{X}\left(\mathbf{LX}\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: $x_i$, the values of the ${\chi }^2$ variates with ${\nu }_i$ degrees of freedom with $x_i=\mathbf{X}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LX}\right)+1$.

Constraint: $\mathbf{X}\left(\mathit{j}\right)\ge 0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{LX}$.

5:     $\mathrm{LDF}$ – INTEGERInput

On entry: the length of the array DF.

Constraint: $\mathbf{LDF}>0$.

6:     $\mathrm{DF}\left(\mathbf{LDF}\right)$ – REAL (KIND=nag_wp) arrayInput

On entry: ${\nu }_i$, the degrees of freedom of the ${\chi }^2$-distribution with ${\nu }_i=\mathbf{DF}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LDF}\right)+1$.

Constraint: $\mathbf{DF}\left(\mathit{j}\right)>0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{LDF}$.

7:     $\mathrm{P}\left(*\right)$ – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array P must be at least $\max \left(\mathbf{LTAIL},\mathbf{LDF},\mathbf{LX}\right)$.

On exit: $p_i$, the probabilities for the ${\chi }^2$ distribution.

8:     $\mathrm{IVALID}\left(*\right)$ – INTEGER arrayOutput

Note: the dimension of the array IVALID must be at least $\max \left(\mathbf{LTAIL},\mathbf{LDF},\mathbf{LX}\right)$.

On exit: $\mathbf{IVALID}\left(i\right)$ indicates any errors with the input arguments, with

$\mathbf{IVALID}\left(i\right)=0$

No error.

$\mathbf{IVALID}\left(i\right)=1$

On entry,

invalid value supplied in TAIL when calculating $p_i$.

$\mathbf{IVALID}\left(i\right)=2$

On entry,

$x_i<0.0$.

$\mathbf{IVALID}\left(i\right)=3$

On entry,

${\nu }_i\le 0.0$.

$\mathbf{IVALID}\left(i\right)=4$

The solution has failed to converge while calculating the gamma variate. The result returned should represent an approximation to the solution.

9:     $\mathrm{IFAIL}$ – INTEGERInput/Output

On entry: IFAIL must be set to $0$, $-1\text{ or }1$. If you are unfamiliar with this parameter you should refer to Section 3.3 in the Essential Introduction for details.

For environments where it might be inappropriate to halt program execution when an error is detected, the value $-1\text{ or }1$ is recommended. If the output of error messages is undesirable, then the value $1$ is recommended. Otherwise, because for this routine the values of the output parameters may be useful even if $\mathbf{IFAIL}\ne \mathbf{0}$ on exit, the recommended value is $-1$. When the value $-\mathbf{1}\text{ or }1$ is used it is essential to test the value of IFAIL on exit.

On exit: $\mathbf{IFAIL}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6  Error Indicators and Warnings

$\mathbf{IFAIL}=1$

On entry, at least one value of X, DF or TAIL was invalid, or the solution failed to converge.
Check IVALID for more information.

$\mathbf{IFAIL}=2$

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LTAIL}>0$.

$\mathbf{IFAIL}=3$

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LX}>0$.

$\mathbf{IFAIL}=4$

On entry, $\text{array size}=〈\mathit{\text{value}}〉$.
Constraint: $\mathbf{LDF}>0$.

$\mathbf{IFAIL}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 3.8 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 3.7 in the Essential Introduction for further information.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

See Section 3.6 in the Essential Introduction for further information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g01scfe.f90)

10.2  Program Data

Program Data (g01scfe.d)

10.3  Program Results

Program Results (g01scfe.r)