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

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"""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