mk_weights.py

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

def weights(vals):

    norm = (vals-np.min(vals))/(np.max(vals)-np.min(vals))

    return norm/np.sum(norm)

x1 = np.linspace(0, 1, 1000)

# Squared weights
y1 = (x1**2)
y1 = weights(np.max(y1)-y1)

# Cubic weights
y2 = (x1**4)
y2 = weights(np.max(y2)-y2)

# Gaussian weights
x2 = np.linspace(stats.halfnorm.ppf(0.01),
                stats.halfnorm.ppf(0.95), 1000)

rv = stats.halfnorm()
y3 = weights(rv.pdf(x2))

# Discrete weights
y4 = x1.copy()
y4[0:801] = 0.8
y4[801:] = 0.2
y4 = weights(y4)

# Piecewise weights
xp1 = np.linspace(stats.halfnorm.ppf(0.01),
                stats.halfnorm.ppf(0.95), 800)

yp1 = rv.pdf(xp1)
yp1 = (yp1-np.min(yp1))/(np.max(yp1)-np.min(yp1))*0.9

xp2 = np.linspace(stats.halfnorm.ppf(0.01),
                stats.halfnorm.ppf(0.95), 200)

yp2 = rv.pdf(xp2)
yp2 = (yp2-np.min(yp2))/(np.max(yp2)-np.min(yp2))*0.1

y5 = y3.copy()
y5[0:800] = yp1+0.9
y5[800:] = yp2+0.1
y5 = y5/np.sum(y5)

x1 = (x1-np.min(x1))/(np.max(x1)-np.min(x1))
x2 = (x2-np.min(x2))/(np.max(x2)-np.min(x2))

fig, ax = plt.subplots(2, sharex=True,sharey=True, figsize=(8,8))
ax[0].plot(x1, y1, 'b', label='Squared')
ax[0].plot(x1, y2, 'r', label='Cubic')
ax[0].plot(x2, y3, 'y', label='Gaussian')
ax[0].legend(loc='upper right')
ax[1].plot(x1, y4, 'c', label='Discrete')
ax[1].plot(x1, y5, 'm', label='Piecewise Gaussian')
ax[1].legend(loc='upper right')
fig.supxlabel('Outlier Likelihood')
fig.supylabel('Weighting')