# Source code for gemseo.uncertainty.statistics.tolerance_interval.uniform

# 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
#
# 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 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