NAG Library Function Document

nag_prob_beta_vector (g01sec)

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[$\mathbf{ltail}$] – const Nag_TailProbabilityInput

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

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

The lower tail probability is returned, i.e., $p_i=P\left(B_i\le {\beta }_i:a_i,b_i\right)$.

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

The upper tail probability is returned, i.e., $p_i=P\left(B_i\ge {\beta }_i:a_i,b_i\right)$.

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

3:     lbeta – IntegerInput

On entry: the length of the array beta.

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

4:     beta[lbeta] – const doubleInput

On entry: ${\beta }_i$, the value of the beta variate with ${\beta }_i=\mathbf{beta}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lbeta}$.

Constraint: $0.0\le \mathbf{beta}\left[\mathit{j}-1\right]\le 1.0$, for $\mathit{j}=1,2,\dots ,\mathbf{lbeta}$.

5:     la – IntegerInput

On entry: the length of the array a.

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

6:     a[la] – const doubleInput

On entry: $a_i$, the first parameter of the required beta distribution with $a_i=\mathbf{a}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{la}$.

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

7:     lb – IntegerInput

On entry: the length of the array b.

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

8:     b[lb] – const doubleInput

On entry: $b_i$, the second parameter of the required beta distribution with $b_i=\mathbf{b}\left[j\right]$, $j=\left(i-1\right)\mathrm{ mod }\mathbf{lb}$.

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

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

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

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

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

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

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,	${\beta }_i<0.0$,
or	${\beta }_i>1.0$.

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

On entry,	$a_i\le 0.0$,
or	$b_i\le 0.0$,

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

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

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

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 beta, a, b or tail was invalid.
Check ivalid for more information.

7  Accuracy

8  Further Comments

9  Example

9.1  Program Text

Program Text (g01sece.c)

9.2  Program Data

Program Data (g01sece.d)

9.3  Program Results

Program Results (g01sece.r)