File:ArgusCDF.svg

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Description
English: CDF of ARGUS distribution. c is 1.
Date
Source Own work
Author Shiyu Ji

Python Source Code

[edit]
# CDF of ARGUS Distribution

import matplotlib.pyplot as pl
import numpy as np
from scipy.special import wofz
import matplotlib.patches as mpatches
import scipy.integrate as integral
from math import pi
from math import exp

t0 = 0.0
dt = 0.001
t_final = 1.0 # also c
c = t_final
T = np.arange(t0, t_final, dt)
ax = pl.figure().add_subplot(111)

# standard normal distribution pdf
def phi(x):
    return exp(-0.5*x*x)/((2*pi)**0.5)

# standard normal distribution cdf
def Phi(x):
    return integral.quad(lambda t: phi(t), -100, x)[0]

def Psi(x):
    return Phi(x) - x*phi(x) - 0.5	

def F(x, chi, c):
    return 1.0-Psi(chi*(1-x*x/c/c)**0.5)/Psi(chi)

def pdf(ax, chi, c, color):
    for t in T:
        old_value = F(t, chi, c)
        new_value = F(t+dt, chi, c)
        ax.plot([t, t+dt], [old_value, new_value], color, linewidth=1.0)

pdf(ax, 0.1, c, 'm-')
pdf(ax, 0.5, c, 'k-')
pdf(ax, 1.0, c, 'b-')
pdf(ax, 2.0, c, 'g-')
pdf(ax, 3.0, c, 'r-')

magentaPatch = mpatches.Patch(color='magenta', label='$\chi=0.1$')
blackPatch = mpatches.Patch(color='black', label='$\chi=0.5$')
bluePatch = mpatches.Patch(color='blue', label='$\chi=1.0$')
greenPatch = mpatches.Patch(color='green', label='$\chi=2.0$')
redPatch = mpatches.Patch(color='red', label='$\chi=3.0$')
pl.legend(handles = [magentaPatch, blackPatch, bluePatch, greenPatch, redPatch], loc=2)

pl.show()

Licensing

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I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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Date/TimeThumbnailDimensionsUserComment
current08:48, 27 May 2017Thumbnail for version as of 08:48, 27 May 2017720 × 540 (930 KB)Shiyu Ji (talk | contribs)correct the legend order
08:43, 27 May 2017Thumbnail for version as of 08:43, 27 May 2017720 × 540 (930 KB)Shiyu Ji (talk | contribs)User created page with UploadWizard

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