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.