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.

Methods

`buildPartition`()	Accessor to the partition in independent marginal sets if any.
`check`()	Give the reasons of uncompatibility of the margins if any.
`getClassName`()	Accessor to the object's name.
`getOptimizationAlgorithm`()	Accessor to the optimization algorithm used for the computation.
`isCompatible`()	Result of the compatibility tests.
`setOptimizationAlgorithm`(solver)	Accessor to the optimization algorithm used for the computation.

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()

buildPartition()¶

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 to build the appropriate maximum entropy order statistics distribution.

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 found.

getClassName()¶

Accessor to the object’s name.

Returns:

getOptimizationAlgorithm()¶

Accessor to the optimization algorithm used for the computation.

Returns:

algoOptimizationAlgorithm: Optimization algorithm used for the computation.

isCompatible()¶

Result of the compatibility tests.

Returns:

resCompatibilitybool: The final result of the 3 compatibility tests with respect to the order constraint.

setOptimizationAlgorithm(solver)¶

Accessor to the optimization algorithm used for the computation.

Parameters:

algoOptimizationAlgorithm: Optimization algorithm to use for the computation.

OpenTURNS