Wilks

class Wilks(*args)

Class to evaluate the Wilks number.

Available constructor:
Wilks(randomVector)
Parameters:

randomVector : RandomVector of dimension 1

Output variable of interest.

Notes

This class is a static class which enables the evaluation of the Wilks number: the minimal sample size N_{\alpha, \beta, i} to perform in order to garantee that the empirical quantile \alpha, noted \tilde{q}_{\alpha} N_{\alpha, \beta, i} evaluated with the (n - i)^{th} maximum of the sample, noted X_{n - i} be greater than the theoretical quantile q_{\alpha} with a probability at least \beta:

\Pset (\tilde{q}_{\alpha} N_{\alpha, \beta, i} > q_{\alpha}) > \beta

where \tilde{q}_{\alpha} N_{\alpha, \beta, i} = X_{n-i}.

Methods

ComputeSampleSize(confidenceLevel[, marginIndex]) Evaluate the size of the sample.
computeQuantileBound(quantileLevel, …[, …]) Evaluate the bound of the quantile.
getClassName() Accessor to the object’s name.
__init__(*args)

x.__init__(…) initializes x; see help(type(x)) for signature

static ComputeSampleSize(confidenceLevel, marginIndex=0)

Evaluate the size of the sample.

Parameters:

alpha : positive float < 1

The order of the quantile we want to evaluate.

beta : positive float < 1

Confidence on the evaluation of the empirical quantile.

i : int

Rank of the maximum which will evaluate the empirical quantile. Default i = 0 (maximum of the sample)

Returns:

w : int

the Wilks number.

computeQuantileBound(quantileLevel, confidenceLevel, marginIndex=0)

Evaluate the bound of the quantile.

Parameters:

alpha : positive float < 1

The order of the quantile we want to evaluate.

beta : positive float < 1

Confidence on the evaluation of the empirical quantile.

i : int

Rank of the maximum which will evaluate the empirical quantile. Default i = 0 (maximum of the sample)

Returns:

q : Point

The estimate of the quantile upper bound for the given quantile level, at the given confidence level and using the given upper statistics.

getClassName()

Accessor to the object’s name.

Returns:

class_name : str

The object class name (object.__class__.__name__).