NAG Toolbox: nag_stat_prob_beta_vector (g01se)

Purpose

Syntax

Description

References

Parameters

Compulsory Input Parameters

1:     $\mathrm{tail}\left(\mathbf{ltail}\right)$ – cell array of strings

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 $\mathit{i}=1,2,\dots ,\max \left(\mathbf{ltail},\mathbf{lbeta},\mathbf{la},\mathbf{lb}\right)$:

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

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

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

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

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

2:     $\mathrm{beta}\left(\mathbf{lbeta}\right)$ – double array

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

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

3:     $\mathrm{a}\left(\mathbf{la}\right)$ – double array

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

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

4:     $\mathrm{b}\left(\mathbf{lb}\right)$ – double array

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

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

Optional Input Parameters

1:     $\mathrm{ltail}$ – int64int32nag_int scalar

Default: the dimension of the array tail.

The length of the array tail.

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

2:     $\mathrm{lbeta}$ – int64int32nag_int scalar

Default: the dimension of the array beta.

The length of the array beta.

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

3:     $\mathrm{la}$ – int64int32nag_int scalar

Default: the dimension of the array a.

The length of the array a.

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

4:     $\mathrm{lb}$ – int64int32nag_int scalar

Default: the dimension of the array b.

The length of the array b.

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

Output Parameters

1:     $\mathrm{p}\left(:\right)$ – double array

The dimension of the array p will be $\max \left(\mathbf{ltail},\mathbf{lbeta},\mathbf{la},\mathbf{lb}\right)$

$p_i$, the probabilities for the beta distribution.

2:     $\mathrm{ivalid}\left(:\right)$ – int64int32nag_int array

The dimension of the array ivalid will be $\max \left(\mathbf{ltail},\mathbf{lbeta},\mathbf{la},\mathbf{lb}\right)$

$\mathbf{ivalid}\left(i\right)$ 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	$b_i\le 0.0$,

3:     $\mathrm{ifail}$ – int64int32nag_int scalar

$\mathbf{ifail}=\mathbf{0}$ unless the function detects an error (see Error Indicators and Warnings).

Error Indicators and Warnings

Cases prefixed with W are classified as warnings and do not generate an error of type NAG:error_n. See nag_issue_warnings.

W  $\mathbf{ifail}=1$

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

   $\mathbf{ifail}=2$

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

   $\mathbf{ifail}=3$

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

   $\mathbf{ifail}=4$

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

   $\mathbf{ifail}=5$

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

   $\mathbf{ifail}=-99$

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

   $\mathbf{ifail}=-399$

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

   $\mathbf{ifail}=-999$

Dynamic memory allocation failed.

Accuracy

Further Comments

Example

Open in the MATLAB editor: g01se_example

function g01se_example


fprintf('g01se example results\n\n');

tail = {'L'; 'L'; 'L'};
x = [0.25; 0.75; 0.5];
a = [1.0;  1.5;  2.0];
b = [2.0;  1.5;  1.0];
% calculate probability
[p, ivalid, ifail] = g01se( ...
                            tail, x, a, b);

fprintf('   x       a       b       p\n');
lx    = numel(x);
la    = numel(a);
lb    = numel(b);
ltail = numel(tail);
len   = max ([lx, la, lb, ltail]);
for i=0:len-1
  fprintf('%6.4f%8.4f%8.4f%8.4f\n', x(mod(i,lx)+1), a(mod(i,la)+1), ...
          b(mod(i,lb)+1), p(i+1));
end

g01se example results

   x       a       b       p
0.2500  1.0000  2.0000  0.4375
0.7500  1.5000  1.5000  0.8045
0.5000  2.0000  1.0000  0.2500