NAG Library Routine Document

G01SKF

1  Purpose

2  Specification

3  Description

4  References

5  Parameters

1:     LL – INTEGERInput

On entry: the length of the array L

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

2:     L(LL) – REAL (KIND=nag_wp) arrayInput

On entry: ${\lambda }_i$, the parameter of the Poisson distribution with ${\lambda }_i=\mathbf{L}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LL}\right)+1$, for $i=1,2,\dots ,\max \left(\mathbf{LL},\mathbf{LK}\right)$.

Constraint: $0.0<\mathbf{L}\left(\mathit{j}\right)\le {10}^6$, for $\mathit{j}=1,2,\dots ,\mathbf{LL}$.

3:     LK – INTEGERInput

On entry: the length of the array K

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

4:     K(LK) – INTEGER arrayInput

On entry: $k_i$, the integer which defines the required probabilities with $k_i=\mathbf{K}\left(j\right)$, $j=\left(\left(i-1\right)\mathrm{ mod }\mathbf{LK}\right)+1$.

Constraint: $\mathbf{K}\left(\mathit{j}\right)\ge 0$, for $\mathit{j}=1,2,\dots ,\mathbf{LK}$.

5:     PLEK($*$) – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array PLEK must be at least $\max \left(\mathbf{LL},\mathbf{LK}\right)$.

On exit: $\mathrm{Prob}\left\{X_i\le k_i\right\}$, the lower tail probabilities.

6:     PGTK($*$) – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array PGTK must be at least $\max \left(\mathbf{LL},\mathbf{LK}\right)$.

On exit: $\mathrm{Prob}\left\{X_i>k_i\right\}$, the upper tail probabilities.

7:     PEQK($*$) – REAL (KIND=nag_wp) arrayOutput

Note: the dimension of the array PEQK must be at least $\max \left(\mathbf{LL},\mathbf{LK}\right)$.

On exit: $\mathrm{Prob}\left\{X_i=k_i\right\}$, the point probabilities.

8:     IVALID($*$) – INTEGER arrayOutput

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

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,

${\lambda }_i\le 0.0$.

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

On entry,

$k_i<0$.

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

On entry,

${\lambda }_i>{10}^6$.

9:     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, if you are not familiar with this parameter, the recommended value is $0$. When the value $-\mathbf{1}\text{ or }\mathbf{1}$ 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 L or K was invalid.
Check IVALID for more information.

$\mathbf{IFAIL}=2$

On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{LL}>0$.

$\mathbf{IFAIL}=3$

On entry, $\text{array size}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{LK}>0$.

$\mathbf{IFAIL}=-999$

Dynamic memory allocation failed.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01skfe.f90)

9.2  Program Data

Program Data (g01skfe.d)

9.3  Program Results

Program Results (g01skfe.r)