NAG Library Function Document

nag_prob_chi_sq_vector (g01scc)

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 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:     lx – IntegerInput

On entry: the length of the array x.

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

4:     x[lx] – 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:     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:     p[$\mathit{dim}$] – 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:     ivalid[$\mathit{dim}$] – 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:     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: $\mathbf{ltail}>0$.

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.

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)