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

# -*- coding: utf-8 -*-
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
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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 typing import Tuple

import openturns as ot
from numpy import array, inf, ndarray
from past.utils import old_div

from gemseo.uncertainty.statistics.tolerance_interval.distribution import (
    ToleranceInterval,
    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, # type: int mean, # type: float std, # type: float ): # type:(...) -> 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(NormalToleranceInterval, self).__init__(size) self.__mean = mean self.__std = std def _compute( self, coverage, # type: float alpha, # type: float size, # type: int side, # type: ToleranceIntervalSide ): # type: (...) -> 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 = old_div(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 = (old_div((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.")