Source code for gemseo.uncertainty.statistics.tolerance_interval.normal

# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
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# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
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# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
# Lesser General Public License for more details.
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# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301, USA.
# Contributors:
#    INITIAL AUTHORS - initial API and implementation and/or initial
#                           documentation
#        :author: Matthias De Lozzo
#    OTHER AUTHORS   - MACROSCOPIC CHANGES
"""Computation of tolerance intervals from a data-fitted normal distribution."""
from __future__ import annotations

import openturns as ot
from numpy import array
from numpy import inf
from numpy import ndarray

from gemseo.uncertainty.statistics.tolerance_interval.distribution import (
    ToleranceInterval,
)
from gemseo.uncertainty.statistics.tolerance_interval.distribution import (
    ToleranceIntervalSide,
)


[docs]class NormalToleranceInterval(ToleranceInterval): """Computation of tolerance intervals from a data-fitted normal distribution. The formulae come from the R library *tolerance* [1]_. .. [1] Derek S. Young, *tolerance: An R Package for Estimating Tolerance Intervals*, Journal of Statistical Software, 36(5), 2010 """ def __init__( self, size: int, mean: float, std: float, ) -> None: """.. # noqa: D205 D212 D415 Args: mean: The estimation of the mean of the normal distribution. std: The estimation of the standard deviation of the normal distribution. """ super().__init__(size) self.__mean = mean self.__std = std def _compute( self, coverage: float, alpha: float, size: int, side: ToleranceIntervalSide, ) -> tuple[ndarray, ndarray]: if side in [ ToleranceIntervalSide.UPPER, ToleranceIntervalSide.LOWER, ]: offset = ot.Normal().computeQuantile(coverage)[0] * size**0.5 student = ot.Student(size - 1, offset, 1.0) student_quantile = student.computeQuantile(1 - alpha)[0] tolerance_factor = student_quantile / size**0.5 if side == ToleranceIntervalSide.UPPER: upper = self.__mean + tolerance_factor * self.__std return array([-inf]), array([upper]) else: lower = self.__mean - tolerance_factor * self.__std return array([lower]), array([inf]) elif side == ToleranceIntervalSide.BOTH: z_p = ot.Normal().computeQuantile((1 + coverage) / 2.0)[0] u_term = (1 + 1.0 / size) ** 0.5 * z_p chi_square = ot.ChiSquare(size - 1) v_term = ((size - 1) / chi_square.computeQuantile(alpha)[0]) ** 0.5 w_term = ( 1 + (size - 3 - chi_square.computeQuantile(alpha)[0]) / (2 * (size + 1) ** 2) ) ** 0.05 tolerance_factor = u_term * v_term * w_term lower = self.__mean - tolerance_factor * self.__std upper = self.__mean + tolerance_factor * self.__std return array([lower]), array([upper]) else: raise ValueError("The type of tolerance interval is incorrect.")