Wilks

class Wilks(*args)

Class to evaluate the Wilks number.

Refer to Estimating a quantile by Wilks’ method.

Parameters:
randomVectorRandomVector 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 guarantee 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(quantileLevel, confidenceLevel)

Evaluate the size of the sample.

computeQuantileBound(quantileLevel, ...[, ...])

Evaluate the bound of the quantile.
__init__(*args)
static ComputeSampleSize(quantileLevel, confidenceLevel, marginIndex=0)

Evaluate the size of the sample.

Parameters:
alphapositive float < 1

The order of the quantile we want to evaluate.

betapositive float < 1

Confidence on the evaluation of the empirical quantile.

iint

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

Returns:
wint

the Wilks number.

computeQuantileBound(quantileLevel, confidenceLevel, marginIndex=0)

Evaluate the bound of the quantile.

Parameters:
alphapositive float < 1

The order of the quantile we want to evaluate.

betapositive float < 1

Confidence on the evaluation of the empirical quantile.

iint

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

Returns:
qPoint

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

Examples using the class

Estimate Wilks and empirical quantile

Estimate Wilks and empirical quantile