gemseo / uncertainty / statistics / tolerance_interval

# lognormal module¶

Computation of tolerance intervals from a data-fitted log-normal distribution.

Classes:

 LogNormalToleranceInterval(size, mean, std, …) Computation of tolerance intervals from a data-fitted log-normal distribution.
class gemseo.uncertainty.statistics.tolerance_interval.lognormal.LogNormalToleranceInterval(size, mean, std, location)[source]

Computation of tolerance intervals from a data-fitted log-normal 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

Initialize self. See help(type(self)) for accurate signature.

Parameters
• size (int) – The number of samples.

• mean (float) – The estimation of the mean of the normal distribution.

• std (float) – The estimation of the standard deviation of the normal distribution.

• mean – The estimation of the mean of the natural logarithm of a log-normal distributed random variable.

• std – The estimation of the standard deviation of the natural logarithm of a log-normal distributed random variable.

• location (float) – The estimation of the location of the log-normal distributed.

Return type

None

Methods:

 compute(coverage[, confidence, side]) Compute a tolerance interval.
compute(coverage, confidence=0.95, side=<ToleranceIntervalSide.BOTH: 3>)[source]

Compute a tolerance interval.

Parameters
• coverage (float) – A minimum percentage of belonging to the TI.

• confidence (float) – A level of confidence in [0,1].

• side (gemseo.uncertainty.statistics.tolerance_interval.distribution.ToleranceIntervalSide) – The type of the tolerance interval characterized by its sides of interest, either a lower-sided tolerance interval $$[a, +\infty[$$, an upper-sided tolerance interval $$]-\infty, b]$$, or a two-sided tolerance interval $$[c, d]$$.

Returns

The tolerance bounds.

Return type

Tuple[numpy.ndarray, numpy.ndarray]