NAG Library Function Document

nag_prob_chi_sq_vector (g01scc)

1  Purpose

2  Specification

3  Description

4  References

5  Arguments

1:    $\mathbf{ltail}$ – IntegerInput

On entry: the length of the array tail.

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

2:    $\mathbf{tail}\left[\mathbf{ltail}\right]$ – const Nag_TailProbabilityInput

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

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

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

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

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

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

3:    $\mathbf{lx}$ – IntegerInput

On entry: the length of the array x.

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

4:    $\mathbf{x}\left[\mathbf{lx}\right]$ – const doubleInput

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

Constraint: $\mathbf{x}\left[\mathit{j}-1\right]\ge 0.0$, for $\mathit{j}=1,2,\dots ,\mathbf{lx}$.

5:    $\mathbf{ldf}$ – IntegerInput

On entry: the length of the array df.

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

6:    $\mathbf{df}\left[\mathbf{ldf}\right]$ – 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:    $\mathbf{p}\left[\mathit{dim}\right]$ – doubleOutput

Note: the dimension, dim, 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:    $\mathbf{ivalid}\left[\mathit{dim}\right]$ – IntegerOutput

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

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 $p_i$.

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

On entry,

$x_i<0.0$.

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

On entry,

${\nu }_i\le 0.0$.

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

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

9:    $\mathbf{fail}$ – 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.
See Section 3.2.1.2 in the Essential Introduction for further information.

NE_ARRAY_SIZE

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

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

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

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.

An unexpected error has been triggered by this function. Please contact NAG.
See Section 3.6.6 in the Essential Introduction for further information.

NE_NO_LICENCE

Your licence key may have expired or may not have been installed correctly.
See Section 3.6.5 in the Essential Introduction for further information.

NW_IVALID

On entry, at least one value of x, df or tail 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 (g01scce.c)

10.2  Program Data

Program Data (g01scce.d)

10.3  Program Results

Program Results (g01scce.r)