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

# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
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#    INITIAL AUTHORS - initial API and implementation and/or initial
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"""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]_. """