NAG Library Function Document

nag_deviates_chi_sq_vector (g01tcc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:     ltail – IntegerInput

On entry: the length of the array tail.

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

2:     tail[ltail] – const Nag_TailProbabilityInput

On entry: indicates which tail the supplied probabilities represent. For $j=\left(\mathit{i}-1\right)\mathrm{ mod }\mathbf{ltail}$, for $\mathit{i}=1,2,\dots ,\max \left(\mathbf{ltail},\mathbf{lp},\mathbf{ldf}\right)$:

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_LowerTail}$

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

$\mathbf{tail}\left[j\right]=\mathrm{Nag\_UpperTail}$

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

Constraint: $\mathbf{tail}\left[\mathit{j}-1\right]=\mathrm{Nag\_LowerTail}$ or $\mathrm{Nag\_UpperTail}$, for $\mathit{j}=1,2,\dots ,\mathbf{ltail}$.

3:     lp – IntegerInput

On entry: the length of the array p.

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

4:     p[lp] – const doubleInput

On entry: $p_i$, the probability of the required ${\chi }^2$-distribution as defined by tail with $p_i=\mathbf{p}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lp}$.

Constraints:

• if $\mathbf{tail}\left[k\right]=\mathrm{Nag\_LowerTail}$, $0.0\le \mathbf{p}\left[\mathit{j}\right]<1.0$;
• otherwise $0.0<\mathbf{p}\left[\mathit{j}\right]\le 1.0$.

Where $k=\left(i-1\right)\mathrm{ mod }\mathbf{ltail}$ and $j=\left(i-1\right)\mathrm{ mod }\mathbf{lp}$.

5:     ldf – IntegerInput

On entry: the length of the array df.

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

6:     df[ldf] – const doubleInput

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

Constraint: $\mathbf{df}\left[\mathit{j}-1\right]>0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{ldf}$.

7:     x[$\mathit{dim}$] – doubleOutput

Note: the dimension, dim, of the array x must be at least $\max \left(\mathbf{ltail},\mathbf{lp},\mathbf{ldf}\right)$.

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

8:     ivalid[$\mathit{dim}$] – IntegerOutput

Note: the dimension, dim, of the array ivalid must be at least $\max \left(\mathbf{ltail},\mathbf{lp},\mathbf{ldf}\right)$.

On exit: $\mathbf{ivalid}\left[i-1\right]$ indicates any errors with the input arguments, with

$\mathbf{ivalid}\left[i-1\right]=0$

No error.

$\mathbf{ivalid}\left[i-1\right]=1$

On entry,

invalid value supplied in tail when calculating $x_{p_i}$.

$\mathbf{ivalid}\left[i-1\right]=2$

On entry,

invalid value for $p_i$.

$\mathbf{ivalid}\left[i-1\right]=3$

On entry,

${\nu }_i\le 0.0$.

$\mathbf{ivalid}\left[i-1\right]=4$

$p_i$ is too close to $0.0$ or $1.0$ for the result to be calculated.

$\mathbf{ivalid}\left[i-1\right]=5$

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

9:     fail – NagError *Input/Output

The NAG error argument (see Section 3.6 in the Essential Introduction).

6  Error Indicators and Warnings

NE_ALLOC_FAIL

Dynamic memory allocation failed.

NE_ARRAY_SIZE

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

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

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

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.

NW_IVALID

On entry, at least one value of tail, p or df was invalid, or the solution failed to converge.
Check ivalid for more information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g01tcce.c)

10.2  Program Data

Program Data (g01tcce.d)

10.3  Program Results

Program Results (g01tcce.r)