NAG FL Interface
g01sef (prob_​beta_​vector)

1 Purpose

2 Specification

3 Description

4 References

5 Arguments

1: $\mathbf{ltail}$ – Integer Input

On entry: the length of the array tail.

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

2: $\mathbf{tail}\left(\mathbf{ltail}\right)$ – Character(1) array Input

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

$\mathbf{tail}\left(j\right)=\text{'L'}$

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

$\mathbf{tail}\left(j\right)=\text{'U'}$

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

Constraint: $\mathbf{tail}\left(\mathit{j}\right)=\text{'L'}$ or $\text{'U'}$, for $\mathit{j}=1,2,\dots ,\mathbf{ltail}$.

3: $\mathbf{lbeta}$ – Integer Input

On entry: the length of the array beta.

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

4: $\mathbf{beta}\left(\mathbf{lbeta}\right)$ – Real (Kind=nag_wp) array Input

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

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

5: $\mathbf{la}$ – Integer Input

On entry: the length of the array a.

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

6: $\mathbf{a}\left(\mathbf{la}\right)$ – Real (Kind=nag_wp) array Input

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

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

7: $\mathbf{lb}$ – Integer Input

On entry: the length of the array b.

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

8: $\mathbf{b}\left(\mathbf{lb}\right)$ – Real (Kind=nag_wp) array Input

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

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

9: $\mathbf{p}\left(*\right)$ – Real (Kind=nag_wp) array Output

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

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

10: $\mathbf{ivalid}\left(*\right)$ – Integer array Output

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

On exit: $\mathbf{ivalid}\left(i\right)$ indicates any errors with the input arguments, with

$\mathbf{ivalid}\left(i\right)=0$

No error.

$\mathbf{ivalid}\left(i\right)=1$

On entry, invalid value supplied in tail when calculating $p_i$.

$\mathbf{ivalid}\left(i\right)=2$

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

$\mathbf{ivalid}\left(i\right)=3$

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

11: $\mathbf{ifail}$ – Integer Input/Output

On entry: ifail must be set to $0$, $\mathrm{-1}$ or $1$ to set behaviour on detection of an error; these values have no effect when no error is detected.

A value of $0$ causes the printing of an error message and program execution will be halted; otherwise program execution continues. A value of $\mathrm{-1}$ means that an error message is printed while a value of $1$ means that it is not.

If halting is not appropriate, the value $\mathrm{-1}$ or $1$ is recommended. If message printing is undesirable, then the value $1$ is recommended. Otherwise, the value $\mathrm{-1}$ is recommended since useful values can be provided in some output arguments even when $\mathbf{ifail}\ne \mathbf{0}$ on exit. When the value $-\mathbf{1}$ or $\mathbf{1}$ is used it is essential to test the value of ifail on exit.

On exit: $\mathbf{ifail}=\mathbf{0}$ unless the routine detects an error or a warning has been flagged (see Section 6).

6 Error Indicators and Warnings

$\mathbf{ifail}=1$

On entry, at least one value of beta, a, b or tail was invalid.
Check ivalid for more information.

$\mathbf{ifail}=2$

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

$\mathbf{ifail}=3$

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

$\mathbf{ifail}=4$

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

$\mathbf{ifail}=5$

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

$\mathbf{ifail}=-99$

An unexpected error has been triggered by this routine. Please contact NAG.

See Section 7 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-399$

Your licence key may have expired or may not have been installed correctly.

See Section 8 in the Introduction to the NAG Library FL Interface for further information.

$\mathbf{ifail}=-999$

Dynamic memory allocation failed.

See Section 9 in the Introduction to the NAG Library FL Interface for further information.

7 Accuracy

8 Parallelism and Performance

9 Further Comments

10 Example

10.1 Program Text

10.2 Program Data

10.3 Program Results