NAG Library Function Document

nag_prob_normal_vector (g01sac)

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 returned probabilities should represent. Letting $Z$ denote a variate from a standard Normal distribution, and $z_i=\frac{x_i-{\mu }_i}{{\sigma }_i}$, then for $j=\left(\mathit{i}-1\right)\mathrm{ mod }\mathbf{ltail}$, for $\mathit{i}=1,2,\dots ,\max \left(\mathbf{lx},\mathbf{ltail},\mathbf{lxmu},\mathbf{lxstd}\right)$:

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

The lower tail probability is returned, i.e., $p_i=P\left(Z\le z_i\right)$.

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

The upper tail probability is returned, i.e., $p_i=P\left(Z\ge z_i\right)$.

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

The two tail (confidence interval) probability is returned, i.e., $p_i=P\left(Z\le \left|z_i\right|\right)-P\left(Z\le -\left|z_i\right|\right)$.

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

The two tail (significance level) probability is returned, i.e., $p_i=P\left(Z\ge \left|z_i\right|\right)+P\left(Z\le -\left|z_i\right|\right)$.

Constraint: $\mathbf{tail}\left[\mathit{j}-1\right]=\mathrm{Nag\_LowerTail}$, $\mathrm{Nag\_UpperTail}$, $\mathrm{Nag\_TwoTailConfid}$ or $\mathrm{Nag\_TwoTailSignif}$, 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 Normal variate values with $x_i=\mathbf{x}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lx}$.

5:     lxmu – IntegerInput

On entry: the length of the array xmu.

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

6:     xmu[lxmu] – const doubleInput

On entry: ${\mu }_i$, the means with ${\mu }_i=\mathbf{xmu}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lxmu}$.

7:     lxstd – IntegerInput

On entry: the length of the array xstd.

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

8:     xstd[lxstd] – const doubleInput

On entry: ${\sigma }_i$, the standard deviations with ${\sigma }_i=\mathbf{xstd}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lxstd}$.

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

9:     p[$\mathit{dim}$] – doubleOutput

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

On exit: $p_i$, the probabilities for the Normal distribution.

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

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

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,

${\sigma }_i\le 0.0$.

11:   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, $\mathbf{ltail}=⟨\mathit{\text{value}}⟩$.
Constraint: $\mathbf{ltail}>0$.

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

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

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

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 or xstd was invalid.
Check ivalid for more information.

7  Accuracy

8  Parallelism and Performance

9  Further Comments

10  Example

10.1  Program Text

Program Text (g01sace.c)

10.2  Program Data

Program Data (g01sace.d)

10.3  Program Results

Program Results (g01sace.r)