Custom distributions#

Custom parametrization of scipy.stats distributions is available in Pykelihood to align with statistical community standards. In a later version of Pykelihood, we aim to include re-parametrization of a base distribution as a feature of the ``Distribution` class. Custom distributions might thus be deprecated in the future.

class Beta(loc=0.0, scale=1.0, alpha=2.0, beta=1.0)#

Beta distribution.

Parameters:

  • loc (float, optional) – Location parameter, by default 0.0.

  • scale (float, optional) – Scale parameter, by default 1.0.

  • alpha (float, optional) – Alpha parameter, by default 2.0.

  • beta (float, optional) – Beta parameter, by default 1.0.

property params_names#

Return the names of the parameters.

class Exponential(loc=0.0, rate=1.0)#

Exponential distribution.

Parameters:

  • loc (float, optional) – Location parameter, by default 0.0.

  • rate (float, optional) – Rate parameter, by default 1.0.

property params_names#

Return the names of the parameters.

class GEV(loc=0.0, scale=1.0, shape=0.0)#

Generalized Extreme Value (GEV) distribution.

Parameters:

  • loc (float, optional) – Location parameter, by default 0.0.

  • scale (float, optional) – Scale parameter, by default 1.0.

  • shape (float, optional) – Shape parameter, by default 0.0.

Notes

This version of the Generalized Extreme Value distribution (GEV) does not have parameters c, loc, scale but loc, scale and shape where shape is -c.

lb_shape(data)#

Calculate the lower bound of the shape parameter.

Parameters:

data (array-like) – Data to calculate the lower bound.

Returns:

Lower bound of the shape parameter.

Return type:

float

property params_names#

Return the names of the parameters.

ub_shape(data)#

Calculate the upper bound of the shape parameter.

Parameters:

data (array-like) – Data to calculate the upper bound.

Returns:

Upper bound of the shape parameter.

Return type:

float

class GPD(loc=0.0, scale=1.0, shape=0.0)#

Generalized Pareto Distribution (GPD).

Parameters:

  • loc (float, optional) – Location parameter, by default 0.0.

  • scale (float, optional) – Scale parameter, by default 1.0.

  • shape (float, optional) – Shape parameter, by default 0.0.

property params_names#

Return the names of the parameters.

class Gamma(loc=0.0, scale=1.0, shape=0.0)#

Gamma distribution.

Parameters:

  • loc (float, optional) – Location parameter, by default 0.0.

  • scale (float, optional) – Scale parameter, by default 1.0.

  • shape (float, optional) – Shape parameter, by default 0.0.

property params_names#

Return the names of the parameters.

class Pareto(loc=0.0, scale=1.0, alpha=1.0)#

Pareto distribution.

Parameters:

  • loc (float, optional) – Location parameter, by default 0.0.

  • scale (float, optional) – Scale parameter, by default 1.0.

  • alpha (float, optional) – Shape parameter, by default 1.0.

property params_names#

Return the names of the parameters.

class TruncatedDistribution(distribution, lower_bound=-inf, upper_bound=inf)#

Truncated distribution.

Parameters:

  • distribution (Distribution) – The base distribution to truncate.

  • lower_bound (float, optional) – Lower bound of the distribution, by default -np.inf.

  • upper_bound (float, optional) – Upper bound of the distribution, by default np.inf.

Raises:

ValueError – If the lower and upper bounds are equal.

cdf(x)#

Cumulative distribution function.

Parameters:

x (Obs) – Data to evaluate.

Returns:

Cumulative distribution values.

Return type:

np.ndarray

fit(*args, **kwargs)#

Fit the instance to the data.

Parameters:

  • args (tuple) – Positional arguments.

  • kwargs (dict) – Keyword arguments.

Returns:

The fitted instance.

Return type:

TruncatedDistribution

isf(q)#

Inverse survival function.

Parameters:

q (Obs) – Quantiles to evaluate.

Returns:

Inverse survival function values.

Return type:

np.ndarray

property params_names#

Get the names of the parameters.

Returns:

The parameter names.

Return type:

tuple[str, …]

pdf(x)#

Probability density function.

Parameters:

x (Obs) – Data to evaluate.

Returns:

Probability density values.

Return type:

np.ndarray

ppf(q)#

Percent point function (inverse of cdf).

Parameters:

q (Obs) – Quantiles to evaluate.

Returns:

Percent point function values.

Return type:

np.ndarray

rvs(size, *args, **kwargs)#

Generate random variates.

Parameters:

  • size (int) – Number of random variates to generate.

  • args (tuple) – Positional arguments.

  • kwargs (dict) – Keyword arguments.

Returns:

Random variates.

Return type:

np.ndarray