# elephant.kernels.EpanechnikovLikeKernel¶

class elephant.kernels.EpanechnikovLikeKernel(sigma, invert=False)[source]

Class for Epanechnikov-like kernels.

$\begin{split}K(t) = \left\{\begin{array}{ll} (3 /(4 d)) (1 - (t / d)^2), & |t| < d \\ 0, & |t| \geq d \end{array} \right.\end{split}$

with $$d = \sqrt{5} \sigma$$ being the half width of the kernel.

The Epanechnikov kernel under full consideration of its axioms has a half width of $$\sqrt{5}$$. Ignoring one axiom also the respective kernel with half width = 1 can be called Epanechnikov kernel. However, arbitrary width of this type of kernel is here preferred to be called ‘Epanechnikov-like’ kernel.

The parameter invert has no effect on symmetric kernels.

Examples

from elephant import kernels
import quantities as pq
import numpy as np
import matplotlib.pyplot as plt

time_array = np.linspace(-3, 3, num=100) * pq.s
kernel = kernels.EpanechnikovLikeKernel(sigma=1*pq.s)
kernel_time = kernel(time_array)
plt.plot(time_array, kernel_time)
plt.title("EpanechnikovLikeKernel with sigma=1s")
plt.xlabel("time, s")
plt.ylabel("kernel, 1/s")
plt.show()

__init__(sigma, invert=False)

Methods

 __init__(sigma[, invert]) boundary_enclosing_area_fraction(fraction) Calculates the boundary $$b$$ so that the integral from $$-b$$ to $$b$$ encloses a certain fraction of the integral over the complete kernel. cdf(time) Cumulative Distribution Function, CDF. icdf(fraction) Inverse Cumulative Distribution Function, ICDF, also known as a quantile. is_symmetric() True for symmetric kernels and False otherwise (asymmetric kernels). median_index(times) Estimates the index of the Median of the kernel.

Attributes

 min_cutoff Half width of the kernel.