naginterfaces.library.stat.init_​vavilov

naginterfaces.library.stat.init_vavilov(rkappa, beta2, mode)

init_vavilov is used to initialize functions pdf_vavilov() and prob_vavilov().

It is intended to be used before a call to pdf_vavilov() or prob_vavilov().

For full information please refer to the NAG Library document for g01zu

https://support.nag.com/numeric/nl/nagdoc_30.2/flhtml/g01/g01zuf.html

Parameters

rkappafloat

The argument $\kappa$ of the function.

beta2float

The argument ${\beta }^2$ of the function.

modeint

If $mode=0$, pdf_vavilov() is to be called after the call to init_vavilov. Otherwise, prob_vavilov() is to be called.

Returns

xlfloat

$x_l$, a threshold value below which ${\varphi }_V(\lambda \text{;}\kappa ,{\beta }^2)$ will be set to zero by pdf_vavilov() and ${\Phi }_V(\lambda \text{;}\kappa ,{\beta }^2)$ will be set to zero by prob_vavilov() if $\lambda <x_l$.

xufloat

$x_u$, a threshold value above which ${\varphi }_V(\lambda \text{;}\kappa ,{\beta }^2)$ will be set to zero by pdf_vavilov() and ${\Phi }_V(\lambda \text{;}\kappa ,{\beta }^2)$ will be set to unity by prob_vavilov() if $\lambda >x_u$.

commdict, communication object

Communication structure.

Raises

NagValueError

(errno $1$)

On entry, $beta2=⟨value⟩$.

Constraint: $beta2\le 1.0$.

(errno $1$)

On entry, $beta2=⟨value⟩$.

Constraint: $beta2\ge 0.0$.

(errno $1$)

On entry, $rkappa=⟨value⟩$.

Constraint: $rkappa\le 10.0$.

(errno $1$)

On entry, $rkappa=⟨value⟩$.

Constraint: $rkappa\ge 0.01$.

(errno $2$)

The initialization has been abandoned due to an internal error. This error exit is unlikely to occur, but if it does change the values of $rkappa$ and/or $beta2$ and rerun init_vavilov.

Notes

init_vavilov initializes the array $comm$[‘rcomm’] for use by pdf_vavilov() or prob_vavilov() in the evaluation of the Vavilov functions ${\varphi }_V(\lambda \text{;}\kappa ,{\beta }^2)$ and ${\Phi }_V(\lambda \text{;}\kappa ,{\beta }^2)$ respectively.

Multiple calls to prob_vavilov() or pdf_vavilov() can be made following a single call to init_vavilov, provided that $rkappa$ or $beta2$ do not change, and that either all calls are to prob_vavilov() or all calls are to pdf_vavilov(). If you wish to call both prob_vavilov() and pdf_vavilov(), then you will need to initialize both separately.

References

Schorr, B, 1974, Programs for the Landau and the Vavilov distributions and the corresponding random numbers, Comp. Phys. Comm. (7), 215–224