make_distribution#

scipy.stats.make_distribution(dist)[source]#

Generate a ContinuousDistribution class from a compatible object

The argument may be an instance of rv_continuous or an instance of another class that satisfies the interface described below.

The returned value is a ContinuousDistribution subclass. Like any subclass of ContinuousDistribution, it must be instantiated (i.e. by passing all shape parameters as keyword arguments) before use. Once instantiated, the resulting object will have the same interface as any other instance of ContinuousDistribution; e.g., scipy.stats.Normal.

Note

make_distribution does not work perfectly with all instances of rv_continuous. Known failures include levy_stable and vonmises, and some methods of some distributions will not support array shape parameters.

Parameters:

distrv_continuous

Instance of rv_continuous OR an instance of any class with the following attributes:

__make_distribution_version__str

A string containing the version number of SciPy in which this interface is defined. The preferred interface may change in future SciPy versions, in which case support for an old interface version may be deprecated and eventually removed.

parametersdict

Each key is the name of a parameter, and the corresponding value is either a dictionary or tuple. If a dictionary, it may have the following items, with default values used for entries which aren’t present.

endpointstuple, default: (-inf, inf)

A tuple defining the lower and upper endpoints of the domain of the parameter; allowable values are floats, the name (string) of another parameter, or a callable taking parameters as keyword only arguments and returning the numerical value of an endpoint for given parameter values.

inclusivetuple of bool, default: (False, False)

A tuple specifying whether the endpoints are included within the domain of the parameter.

typicaltuple, default: endpoints

Defining endpoints of a typical range of values of a parameter. Can be used for sampling parameter values for testing. Behaves like the endpoints tuple above, and should define a subinterval of the domain given by endpoints.

A tuple value (a, b) is equivalent to {endpoints: (a, b)}.

supportdict or tuple

A dictionary describing the support of the distribution or a tuple describing the endpoints of the support. This behaves identically to the values of the parameters dict described above, except that the key typical is ignored.

The class must also define a pdf method and may define methods logentropy, entropy, median, mode, logpdf, logcdf, cdf, logccdf, ccdf, ilogcdf, icdf, ilogccdf, iccdf, moment, and sample. If defined, these methods must accept the parameters of the distribution as keyword arguments and also accept any positional-only arguments accepted by the corresponding method of ContinuousDistribution. The moment method must accept the order and kind arguments by position or keyword, but may return None if a formula is not available for the arguments; in this case, the infrastructure will fall back to a default implementation. The sample method must accept shape by position or keyword, but contrary to the public method of the same name, the argument it receives will be the full shape of the output array - that is, the shape passed to the public method prepended to the broadcasted shape of random variable parameters.

Returns:

CustomDistributionContinuousDistribution

A subclass of ContinuousDistribution corresponding with dist. The initializer requires all shape parameters to be passed as keyword arguments (using the same names as the instance of rv_continuous).

Notes

The documentation of ContinuousDistribution is not rendered. See below for an example of how to instantiate the class (i.e. pass all shape parameters of dist to the initializer as keyword arguments). Documentation of all methods is identical to that of scipy.stats.Normal. Use help on the returned class or its methods for more information.

Examples

Try it in your browser!

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy import stats

Create a ContinuousDistribution from scipy.stats.loguniform.

>>> LogUniform = stats.make_distribution(stats.loguniform)
>>> X = LogUniform(a=1.0, b=3.0)
>>> np.isclose((X + 0.25).median(), stats.loguniform.ppf(0.5, 1, 3, loc=0.25))
np.True_
>>> X.plot()
>>> sample = X.sample(10000, rng=np.random.default_rng())
>>> plt.hist(sample, density=True, bins=30)
>>> plt.legend(('pdf', 'histogram'))
>>> plt.show()

Create a custom distribution.

>>> class MyLogUniform:
...     @property
...     def __make_distribution_version__(self):
...         return "1.16.0"
...
...     @property
...     def parameters(self):
...         return {'a': {'endpoints': (0, np.inf),
...                       'inclusive': (False, False)},
...                 'b': {'endpoints': ('a', np.inf),
...                       'inclusive': (False, False)}}
...
...     @property
...     def support(self):
...         return {'endpoints': ('a', 'b'), 'inclusive': (True, True)}
...
...     def pdf(self, x, a, b):
...         return 1 / (x * (np.log(b)- np.log(a)))
>>>
>>> MyLogUniform = stats.make_distribution(MyLogUniform())
>>> Y = MyLogUniform(a=1.0, b=3.0)
>>> np.isclose(Y.cdf(2.), X.cdf(2.))
np.True_

Create a custom distribution with variable support.

>>> class MyUniformCube:
...     @property
...     def __make_distribution_version__(self):
...         return "1.16.0"
...
...     @property
...     def parameters(self):
...         return {"a": (-np.inf, np.inf), 
...                 "b": {'endpoints':('a', np.inf), 'inclusive':(True, False)}}
...
...     @property
...     def support(self):
...         def left(*, a, b):
...             return a**3
...
...         def right(*, a, b):
...             return b**3
...         return (left, right)
...
...     def pdf(self, x, *, a, b):
...         return 1 / (3*(b - a)*np.cbrt(x)**2)
...
...     def cdf(self, x, *, a, b):
...         return (np.cbrt(x) - a) / (b - a)
>>>
>>> MyUniformCube = stats.make_distribution(MyUniformCube())
>>> X = MyUniformCube(a=-2, b=2)
>>> Y = stats.Uniform(a=-2, b=2)**3
>>> X.support()
(-8.0, 8.0)
>>> np.isclose(X.cdf(2.1), Y.cdf(2.1))
np.True_

Go BackOpen In Tab