OrderStatisticsMarginalChecker¶

class OrderStatisticsMarginalChecker(*args)¶

Compatibility tests of marginals with respect to the order statistics constraint.

Parameters

collsequence of Distribution: The marginals $(F_1, \dots, F_n)$ which are tested with respect to the order $F_1 < \dots < F_n$ in the context of the maximum order statistics distribution.

Notes

Three tests are performed. We note $[a_i,b_i]$ the range of $X_i$ . The tests are :

Test 1 checks that $a_i \leq a_{i+1}$ and $b_i \leq b_{i+1}$ for all $i$ .
Test 2 discretizes $[0,1]$ with $\{\dfrac{1}{2n},\dfrac{3}{2n}, \dots,\dfrac{2n-1}{2n}\} = \{q_1, \dots, q_{2n-1} \}$ where $n$ is defined in the ResourceMap with OSMC-OptimizationEpsilon. By default, $n=100$ . Test 2 checks that:

$F_k^{-1}(q_j) \geq F_{k-1}^{-1}(q_j)+\epsilon, \quad 1 \leq j \leq d$

where $\epsilon$ is defined in the ResourceMap with OSMC-QuantileIteration. By default, $\epsilon=10^{-7}$ .
Test 3 checks that:

$\min_{q \in [q_{j-1}, q_j]} \{F_k^{-1}(q) - F_{k-1}^{-1}(q) \} \geq \epsilon$

using the TNC algorithm.

Examples

Create the test checker:

>>> import openturns as ot
>>> coll = [ot.Uniform(-1.0, 1.0), ot.Uniform(-0.5, 1.5)]
>>> testChecker = ot.OrderStatisticsMarginalChecker(coll)

Check the compatibility:

>>> compatibilityResult = testChecker.isCompatible()

Methods

`buildPartition`(self)	Accessor to the partition in independent marginal sets if any.
`check`(self)	Give the reasons of uncompatibility of the margins if any.
`getClassName`(self)	Accessor to the object’s name.
`isCompatible`(self)	Result of the compatibility tests.

getOptimizationAlgorithm
setOptimizationAlgorithm

__init__(self, \*args)¶: Initialize self. See help(type(self)) for accurate signature.

buildPartition(self)¶

Accessor to the partition in independent marginal sets if any.

Returns

indepMarginalsIndices: Indicates the indices that build some independent sets of marginals. If we note $indepMarginals = [i_1, i_2]$ then the sub random vectors $(X_1, \dots, X_{i_1})$ , $(X_{i_1+1}, \dots, X_{i_2})$ and $(X_{i_2+1}, \dots, X_n)$ are independent. This information is automatically used by OpenTURNS to build the appropriated maximum entropy order statistics distribution.