Source code for statsmodels.distributions.empirical_distribution
"""
Empirical CDF Functions
"""
import numpy as np
from scipy.interpolate import interp1d
def _conf_set(F, alpha=.05):
r"""
Constructs a Dvoretzky-Kiefer-Wolfowitz confidence band for the eCDF.
Parameters
----------
F : array_like
The empirical distributions
alpha : float
Set alpha for a (1 - alpha) % confidence band.
Notes
-----
Based on the DKW inequality.
.. math:: P \left( \sup_x \left| F(x) - \hat(F)_n(X) \right| >
\epsilon \right) \leq 2e^{-2n\epsilon^2}
References
----------
Wasserman, L. 2006. `All of Nonparametric Statistics`. Springer.
"""
nobs = len(F)
epsilon = np.sqrt(np.log(2./alpha) / (2 * nobs))
lower = np.clip(F - epsilon, 0, 1)
upper = np.clip(F + epsilon, 0, 1)
return lower, upper
[docs]
class StepFunction:
"""
A basic step function.
Values at the ends are handled in the simplest way possible:
everything to the left of x[0] is set to ival; everything
to the right of x[-1] is set to y[-1].
Parameters
----------
x : array_like
y : array_like
ival : float
ival is the value given to the values to the left of x[0]. Default
is 0.
sorted : bool
Default is False.
side : {'left', 'right'}, optional
Default is 'left'. Defines the shape of the intervals constituting the
steps. 'right' correspond to [a, b) intervals and 'left' to (a, b].
Examples
--------
>>> import numpy as np
>>> from statsmodels.distributions.empirical_distribution import (
>>> StepFunction)
>>>
>>> x = np.arange(20)
>>> y = np.arange(20)
>>> f = StepFunction(x, y)
>>>
>>> print(f(3.2))
3.0
>>> print(f([[3.2,4.5],[24,-3.1]]))
[[ 3. 4.]
[ 19. 0.]]
>>> f2 = StepFunction(x, y, side='right')
>>>
>>> print(f(3.0))
2.0
>>> print(f2(3.0))
3.0
"""
def __init__(self, x, y, ival=0., sorted=False, side='left'): # noqa
if side.lower() not in ['right', 'left']:
msg = "side can take the values 'right' or 'left'"
raise ValueError(msg)
self.side = side
_x = np.asarray(x)
_y = np.asarray(y)
if _x.shape != _y.shape:
msg = "x and y do not have the same shape"
raise ValueError(msg)
if len(_x.shape) != 1:
msg = 'x and y must be 1-dimensional'
raise ValueError(msg)
self.x = np.r_[-np.inf, _x]
self.y = np.r_[ival, _y]
if not sorted:
asort = np.argsort(self.x)
self.x = np.take(self.x, asort, 0)
self.y = np.take(self.y, asort, 0)
self.n = self.x.shape[0]
def __call__(self, time):
tind = np.searchsorted(self.x, time, self.side) - 1
return self.y[tind]
[docs]
class ECDF(StepFunction):
"""
Return the Empirical CDF of an array as a step function.
Parameters
----------
x : array_like
Observations
side : {'left', 'right'}, optional
Default is 'right'. Defines the shape of the intervals constituting the
steps. 'right' correspond to [a, b) intervals and 'left' to (a, b].
Returns
-------
Empirical CDF as a step function.
Examples
--------
>>> import numpy as np
>>> from statsmodels.distributions.empirical_distribution import ECDF
>>>
>>> ecdf = ECDF([3, 3, 1, 4])
>>>
>>> ecdf([3, 55, 0.5, 1.5])
array([ 0.75, 1. , 0. , 0.25])
"""
def __init__(self, x, side='right'):
x = np.array(x, copy=True)
x.sort()
nobs = len(x)
y = np.linspace(1./nobs, 1, nobs)
super().__init__(x, y, side=side, sorted=True)
# TODO: make `step` an arg and have a linear interpolation option?
# This is the path with `step` is True
# If `step` is False, a previous version of the code read
# `return interp1d(x,y,drop_errors=False,fill_values=ival)`
# which would have raised a NameError if hit, so would need to be
# fixed. See GH#5701.
[docs]
class ECDFDiscrete(StepFunction):
"""
Return the Empirical Weighted CDF of an array as a step function.
Parameters
----------
x : array_like
Data values. If freq_weights is None, then x is treated as observations
and the ecdf is computed from the frequency counts of unique values
using nunpy.unique.
If freq_weights is not None, then x will be taken as the support of the
mass point distribution with freq_weights as counts for x values.
The x values can be arbitrary sortable values and need not be integers.
freq_weights : array_like
Weights of the observations. sum(freq_weights) is interpreted as nobs
for confint.
If freq_weights is None, then the frequency counts for unique values
will be computed from the data x.
side : {'left', 'right'}, optional
Default is 'right'. Defines the shape of the intervals constituting the
steps. 'right' correspond to [a, b) intervals and 'left' to (a, b].
Returns
-------
Weighted ECDF as a step function.
Examples
--------
>>> import numpy as np
>>> from statsmodels.distributions.empirical_distribution import (
>>> ECDFDiscrete)
>>>
>>> ewcdf = ECDFDiscrete([3, 3, 1, 4])
>>> ewcdf([3, 55, 0.5, 1.5])
array([0.75, 1. , 0. , 0.25])
>>>
>>> ewcdf = ECDFDiscrete([3, 1, 4], [1.25, 2.5, 5])
>>>
>>> ewcdf([3, 55, 0.5, 1.5])
array([0.42857143, 1., 0. , 0.28571429])
>>> print('e1 and e2 are equivalent ways of defining the same ECDF')
e1 and e2 are equivalent ways of defining the same ECDF
>>> e1 = ECDFDiscrete([3.5, 3.5, 1.5, 1, 4])
>>> e2 = ECDFDiscrete([3.5, 1.5, 1, 4], freq_weights=[2, 1, 1, 1])
>>> print(e1.x, e2.x)
[-inf 1. 1.5 3.5 4. ] [-inf 1. 1.5 3.5 4. ]
>>> print(e1.y, e2.y)
[0. 0.2 0.4 0.8 1. ] [0. 0.2 0.4 0.8 1. ]
"""
def __init__(self, x, freq_weights=None, side='right'):
if freq_weights is None:
x, freq_weights = np.unique(x, return_counts=True)
else:
x = np.asarray(x)
assert len(freq_weights) == len(x)
w = np.asarray(freq_weights)
sw = np.sum(w)
assert sw > 0
ax = x.argsort()
x = x[ax]
y = np.cumsum(w[ax])
y = y / sw
super().__init__(x, y, side=side, sorted=True)
[docs]
def monotone_fn_inverter(fn, x, vectorized=True, **keywords):
"""
Given a monotone function fn (no checking is done to verify monotonicity)
and a set of x values, return an linearly interpolated approximation
to its inverse from its values on x.
"""
x = np.asarray(x)
if vectorized:
y = fn(x, **keywords)
else:
y = []
for _x in x:
y.append(fn(_x, **keywords))
y = np.array(y)
a = np.argsort(y)
return interp1d(y[a], x[a])
Last update:
Apr 16, 2024