1%feature("docstring") OT::Wilks
2"Class to evaluate the Wilks number.
3
4Refer to :ref:`quantile_estimation_wilks`.
5
6Parameters
7----------
8randomVector : :class:`~openturns.RandomVector` of dimension 1
9    Output variable of interest.
10
11Notes
12-----
13This class is a static class which enables the evaluation of the Wilks number:
14the minimal sample size :math:`N_{\alpha, \beta, i}` to perform in order to
15guarantee that the empirical quantile :math:`\alpha`, noted
16:math:`\tilde{q}_{\alpha} N_{\alpha, \beta, i}` evaluated with the
17:math:`(n - i)^{th}` maximum of the sample, noted :math:`X_{n - i}` be greater
18than the theoretical quantile :math:`q_{\alpha}` with a probability at least
19:math:`\beta`:
20
21.. math::
22
23    \Pset (\tilde{q}_{\alpha} N_{\alpha, \beta, i} > q_{\alpha}) > \beta
24
25where :math:`\tilde{q}_{\alpha} N_{\alpha, \beta, i} = X_{n-i}`."
26
27// ---------------------------------------------------------------------
28
29%feature("docstring") OT::Wilks::ComputeSampleSize
30"Evaluate the size of the sample.
31
32Parameters
33----------
34alpha : positive float :math:`< 1`
35    The order of the quantile we want to evaluate.
36beta : positive float :math:`< 1`
37    Confidence on the evaluation of the empirical quantile.
38i : int
39    Rank of the maximum which will evaluate the empirical quantile. Default
40    :math:`i = 0` (maximum of the sample)
41
42Returns
43-------
44w : int
45    the Wilks number."
46
47// ---------------------------------------------------------------------
48
49%feature("docstring") OT::Wilks::computeQuantileBound
50"Evaluate the bound of the quantile.
51
52Parameters
53----------
54alpha : positive float :math:`< 1`
55    The order of the quantile we want to evaluate.
56beta : positive float :math:`< 1`
57    Confidence on the evaluation of the empirical quantile.
58i : int
59    Rank of the maximum which will evaluate the empirical quantile. Default
60    :math:`i = 0` (maximum of the sample)
61
62Returns
63-------
64q : :class:`~openturns.Point`
65    The estimate of the quantile upper bound for the given quantile level, at
66    the given confidence level and using the given upper statistics."
67