Source code for gemseo.uncertainty.statistics.tolerance_interval.uniform
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
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# 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
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# 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 uniform distribution."""
from __future__ import annotations
from gemseo.uncertainty.statistics.tolerance_interval.distribution import (
ToleranceInterval,
)
[docs]class UniformToleranceInterval(ToleranceInterval):
"""Computation of tolerance intervals from a data-fitted uniform 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,
minimum: float,
maximum: float,
) -> None:
""".. # noqa: D205 D212 D415
Args:
minimum: The estimation of the lower bound of the uniform distribution.
maximum: The estimation of the upper bound of the uniform distribution.
"""
super().__init__(size)
self.__minimum = minimum
self.__maximum = maximum
def _compute_lower_bound(
self,
coverage: float,
alpha: float,
size: int,
) -> float:
return self.__compute_exponential_bound(1 - coverage, 1 - alpha, size)
def _compute_upper_bound(
self,
coverage: float,
alpha: float,
size: int,
) -> float:
return self.__compute_exponential_bound(coverage, alpha, size)
def __compute_exponential_bound(
self,
coverage: float,
alpha: float,
size: int,
) -> float:
"""Compute a bound of the tolerance interval for a uniform distribution.
Args:
coverage: A minimum percentage of belonging to the TI.
alpha: ``1-alpha`` is the level of confidence in [0,1].
size: The number of samples.
Returns:
The bound of the tolerance interval.
"""
coefficient = coverage / alpha ** (1.0 / size)
return (self.__maximum - self.__minimum) * coefficient + self.__minimum