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(object): """ 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'): 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]
[docs] 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(ECDF, self).__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]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])
if __name__ == "__main__": #TODO: Make sure everything is correctly aligned and make a plotting # function from statsmodels.compat.python import urlopen import matplotlib.pyplot as plt nerve_data = urlopen('http://www.statsci.org/data/general/nerve.txt') nerve_data = np.loadtxt(nerve_data) x = nerve_data / 50. # was in 1/50 seconds cdf = ECDF(x) x.sort() F = cdf(x) plt.step(x, F, where='post') lower, upper = _conf_set(F) plt.step(x, lower, 'r', where='post') plt.step(x, upper, 'r', where='post') plt.xlim(0, 1.5) plt.ylim(0, 1.05) plt.vlines(x, 0, .05) plt.show()