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

# 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 exponential distribution."""
from __future__ import annotations

import openturns as ot

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


[docs]class ExponentialToleranceInterval(ToleranceInterval): """Computation of tolerance intervals from a data-fitted exponential 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, rate: float, location: float, ) -> None: """.. # noqa: D205 D212 D415 Args: rate: The estimation of the rate of the exponential distribution. location: The estimation of the location of the exponential distribution. """ super().__init__(size) self.__rate = rate self.__location = location def _compute_lower_bound( self, coverage: float, alpha: float, size: int, ) -> float: k_1 = 1 - (coverage**size / alpha) ** (1.0 / (size - 1)) return self.__location + k_1 / self.__rate def _compute_upper_bound( self, coverage: float, alpha: float, size: int, ) -> float: chi2_num = ot.ChiSquare(2).computeQuantile(coverage)[0] chi2_den = ot.ChiSquare(2 * size - 2).computeQuantile(coverage)[0] k_2 = size * chi2_num / chi2_den return self.__location + k_2 / self.__rate