/usr/include/openturns/swig/OrderStatisticsMarginalChecker_doc.i is in libopenturns-dev 1.7-3.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 | %feature("docstring") OT::OrderStatisticsMarginalChecker
"Compatibility tests of marginals with respect to the order statistics constraint.
Parameters
----------
coll : sequence of :class:`~openturns.Distribution`
The marginals :math:`(F_1, \\\\dots, F_n)` which are tested with respect to the order :math:`F_1 < \\\\dots < F_n` in the context of the maximum order statistics distribution.
Notes
-----
Three tests are performed. We note :math:`[a_i,b_i]` the range of :math:`X_i`. The tests are :
- Test 1 checks that :math:`a_i \\\\leq a_{i+1}` and :math:`b_i \\\\leq b_{i+1}` for all :math:`i`.
- Test 2 discretizes :math:`[0,1]` with :math:`\\\\{\\\\dfrac{1}{2n},\\\\dfrac{3}{2n}, \\\\dots,\\\\dfrac{2n-1}{2n}\\\\} = \\\\{q_1, \\\\dots, q_{2n-1} \\\\}` where :math:`n` is defined in the :class:`~openturns.ResourceMap` with `OSMC-OptimizationEpsilon`. By default, :math:`n=100`. Test 2 checks that:
.. math::
F_k^{-1}(q_j) \\\\geq F_{k-1}^{-1}(q_j)+\\\\epsilon, \\\\quad 1 \\\\leq j \\\\leq d
where :math:`\\\\epsilon` is defined in the :class:`~openturns.ResourceMap` with `OSMC-QuantileIteration`. By default, :math:`\\\\epsilon=10^{-7}`.
- Test 3 checks that:
.. math::
\\\\min_{q \\\\in [q_{j-1}, q_j]} \\\\{F_k^{-1}(q) - F_{k-1}^{-1}(q) \\\\} \\\\geq \\\\epsilon
using the TNC algorithm.
Examples
--------
Create the test checker:
>>> import openturns as ot
>>> coll = [ot.Uniform(-1., 1.), ot.Uniform(-0.5, 1.5)]
>>> testChecker = ot.OrderStatisticsMarginalChecker(coll)
Check the compatibility:
>>> compatibilityResult = testChecker.isCompatible()"
// ---------------------------------------------------------------------
%feature("docstring") OT::OrderStatisticsMarginalChecker::isCompatible
"Result of the compatibility tests.
Returns
-------
resCompatibility : bool
The final result of the 3 compatibility tests with respect to the order constraint."
// ---------------------------------------------------------------------
%feature("docstring") OT::OrderStatisticsMarginalChecker::check
"Give the reasons of uncompatibility of the margins if any.
Notes
-----
This method throws an exception in case of compatibility problem with a message indicating the first compatibility problem arised.
"
// ---------------------------------------------------------------------
%feature("docstring") OT::OrderStatisticsMarginalChecker::buildPartition
"Accessor to the partition in independent marginal sets if any.
Returns
-------
indepMarginals : :class:`~openturns.Indices`
Indicates the indices that build some independent sets of marginals. If we note :math:`indepMarginals = [i_1, i_2]` then the sub random vectors :math:`(X_1, \\\\dots, X_{i_1})`, :math:`(X_{i_1+1}, \\\\dots, X_{i_2})` and :math:`(X_{i_2+1}, \\\\dots, X_n)` are independent.
This information is automatically used by OpenTURNS to build the appropriated maximum entropy order statistics distribution."
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