axtreme.utils.distibution_helpers

Helper for working with scipy distibutions.

Functions

distribution_parameter_names_from_scipy(dist)

Collects the parameters required for a scipy rv_continous distibution.

fit_dist_with_uncertainty(data, dist)

Fit a distibution, returning the parameters estimate and Gaussian uncertainty of the fit.
axtreme.utils.distibution_helpers.distribution_parameter_names_from_scipy(dist: rv_continuous) → list[str]

Collects the parameters required for a scipy rv_continous distibution.

Withing axtreme this is used to determine what a GP should predict.

Parameters:

dist – The distibution to retrieve the parameters for.

Returns:

The distibutiion parameter names, IN THE ORDER they should be passed to calls to this distibution class. For example:

  • gumbel_r.pdf(x, loc=0, scale=1) -> order returned [‘loc’,’scale’]

  • weibull_max.pdf(x, c, loc=0, scale=1) -> order returned [‘c’,’loc’,’scale’]

axtreme.utils.distibution_helpers.fit_dist_with_uncertainty(data: Buffer | _SupportsArray[dtype[Any]] | _NestedSequence[_SupportsArray[dtype[Any]]] | bool | int | float | complex | str | bytes | _NestedSequence[bool | int | float | complex | str | bytes], dist: rv_continuous) → tuple[ndarray[tuple[int], dtype[float64]], ndarray[tuple[int, int], dtype[float64]]]

Fit a distibution, returning the parameters estimate and Gaussian uncertainty of the fit.

Results of fitting with Maximum Likelihood give a normal distibution where

  • mean:parameter estimate

  • covariance matrix: Uncertainty in estimate (Inverse Fischer infomation matrix)

Note

Parameters are returned in tha same order they appear in the fucntion calls of this call. For example, weibull_max.pdf(x, c, loc=0, scale=1) -> order returned [‘c’,’loc’,’scale’] This order can be extracted with the helper function distribution_parameter_names_from_scipy

Parameters:

  • data (ArrayLike) – 1 dimensional set of data to fit a distibution to.

  • dist (rv_continuous) – the distribution to be fitted.

Returns:

(n) parameter mean estimates covariance: (n,n) covariance matrix of the uncertainty in parameters fitted

Return type:

feature mean

Todo

  • Some distributions have convergence issues. Currently only allow gumble_r.

  • Optimisation method needs thorough testing