gemseo / uncertainty / statistics / tolerance_interval

# lognormal module¶

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].

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

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

• std (float) – 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.

class Bounds(lower, upper)

Bases: NamedTuple

The component-wise bounds of a vector.

Create new instance of Bounds(lower, upper)

Parameters:
count(value, /)

Return number of occurrences of value.

index(value, start=0, stop=9223372036854775807, /)

Return first index of value.

Raises ValueError if the value is not present.

lower: ndarray[Any, dtype[float]]

Alias for field number 0

upper: ndarray[Any, dtype[float]]

Alias for field number 1

class ToleranceIntervalSide(value)

Bases: LowercaseStrEnum

The side of the tolerance interval.

BOTH = 'both'
LOWER = 'lower'
UPPER = 'upper'
compute(coverage, confidence=0.95, side=ToleranceIntervalSide.BOTH)[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].

By default it is set to 0.95.

• side (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 $$[c, d]$$.

By default it is set to “both”.

Returns:

The tolerance bounds.

Return type:

Bounds