File:ArgusPDF.svg

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Summary

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

Python Source Code

# PDF 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 f(x, chi, c):
    return (chi**3)/((Phi(chi)-chi*phi(chi)-0.5) \
            *(2*pi)**0.5)*x/c/c*((1.0-x*x/c/c)**0.5) \
            *exp(-chi*chi*(1.0-x*x/c/c)/2.0)

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()

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27 May 2017

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Date/TimeThumbnailDimensionsUserComment
current08:49, 27 May 2017Thumbnail for version as of 08:49, 27 May 2017720 × 540 (936 KB)Shiyu Jicorrect the legend order.
08:43, 27 May 2017Thumbnail for version as of 08:43, 27 May 2017720 × 540 (936 KB)Shiyu JiUser created page with UploadWizard

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