Source code for gemseo.uncertainty.statistics.tolerance_interval.weibull
# 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
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# 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 Weibull distribution."""
from __future__ import annotations
import openturns as ot
from numpy import exp
from numpy import log
from gemseo.uncertainty.statistics.tolerance_interval.distribution import (
ToleranceInterval,
)
[docs]
class WeibullToleranceInterval(ToleranceInterval):
"""Computation of tolerance intervals from a data-fitted Weibull 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,
scale: float,
shape: float,
location: float,
) -> None:
"""
Args:
scale: The estimation of the scale of the Weibull distribution.
shape: The estimation of the shape of the Weibull distribution.
location: The estimation of the location of the Weibull distribution.
""" # noqa: D205 D212 D415
super().__init__(size)
self.__scale = scale
self.__shape = shape
self.__location = location
@staticmethod
def __lambda_function(
value: float,
) -> float:
"""Compute the natural logarithm of the opposite natural logarithm.
Args:
value: The value to be transformed.
Returns:
The transformed value.
"""
return log(-log(value))
def _compute_lower_bound(
self,
coverage: float,
alpha: float,
size: int,
) -> float:
xi_ = log(self.__scale)
delta = 1.0 / self.__shape
offset = -(size**0.5) * self.__lambda_function(coverage)
student = ot.Student(size - 1, offset, 1.0)
bound = xi_ - delta * student.computeQuantile(1 - alpha)[0] / (size - 1) ** 0.5
return exp(bound) + self.__location
def _compute_upper_bound(
self,
coverage: float,
alpha: float,
size: int,
) -> float:
xi_ = log(self.__scale)
delta = 1.0 / self.__shape
offset = -(size**0.5) * self.__lambda_function(1 - coverage)
student = ot.Student(size - 1, offset, 1.0)
bound = xi_ - delta * student.computeQuantile(alpha)[0] / (size - 1) ** 0.5
return exp(bound) + self.__location
[docs]
class WeibullMinToleranceInterval(WeibullToleranceInterval):
"""Computation of tolerance intervals from a data-fitted Weibull distribution.
The formulae come from the R library *tolerance* [1]_.
"""