File:Generalized normal cdfs.svg
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Summary
[edit]DescriptionGeneralized normal cdfs.svg |
English: Plots of the cumulative distribution functions for several members of the family of generalized normal probability distributions. |
Date | |
Source | Own work |
Author | Skbkekas |
SVG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python code##
## Python code to generate density and CDF plots for the
## generalized normal distribution (requires matplotlib, numpy,
## and the special functions module of scipy).
##
import matplotlib.pyplot as plt
import numpy as np
import scipy.special as sp
def dens(X, a, b, mu):
Y = np.abs(X-mu)/a
Y = np.exp(-Y**b)
Y = Y*b/(2*a)
Y /= np.exp(sp.gammaln(1/float(b)))
return Y
def cdf(X, a, b, mu):
Y = (np.abs(X-mu)/a)**b
Y = sp.gammainc(1/float(b),Y)
Y = Y * np.sign(X-mu) / 2 + 0.5
return Y
w = 1.5
X = np.arange(-3, 3, 0.01)
plt.clf()
colors = ['aqua', 'black', 'lime', 'deeppink', 'darkorange', 'blue']
B = [0.5, 1, 1.5, 2, 3, 8]
F = []
for c,b in zip(colors, B):
Y = dens(X, 1, b, 0)
f = plt.plot(X, Y, '-', color=c, lw=w)
F.append(f)
plt.hold(True)
s = ["$\\beta=%s$" % b for b in B]
b = plt.legend(tuple(F), tuple(s), 'upper left')
plt.ylabel("Density")
b.draw_frame(False)
plt.savefig("generalized_normal_densities.svg")
plt.savefig("generalized_normal_densities.png")
plt.clf()
F = []
for c,b in zip(colors, B):
Y = cdf(X, 1, b, 0)
f = plt.plot(X, Y, '-', color=c, lw=w)
F.append(f)
plt.hold(True)
b = plt.legend(tuple(F), tuple(s), 'upper left')
plt.ylabel("Cumulative probability")
b.draw_frame(False)
plt.ylim(0,1)
plt.savefig("generalized_normal_cdfs.svg")
plt.savefig("generalized_normal_cdfs.png")
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Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported license. | ||
| ||
This licensing tag was added to this file as part of the GFDL licensing update.http://creativecommons.org/licenses/by-sa/3.0/CC BY-SA 3.0Creative Commons Attribution-Share Alike 3.0truetrue |
Copyleft: This work of art is free; you can redistribute it and/or modify it according to terms of the Free Art License. You will find a specimen of this license on the Copyleft Attitude site as well as on other sites. http://artlibre.org/licence/lal/enFALFree Art Licensefalsetrue |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 00:41, 28 April 2015 | 720 × 540 (30 KB) | Jugander (talk | contribs) | Re-generated using modern Python with fixed Gamma function (correcting an error observed on the talk page). | |
04:06, 28 February 2009 | 720 × 540 (114 KB) | Skbkekas (talk | contribs) | {{Information |Description={{en|1=Cumulative distribution functions for various generalized normal distributions.}} |Source=Own work by uploader |Author=Skbkekas |Date=2009-02-27 |Permission= |other_versions= }} <!--{{ImageUpload|full}} |
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Width | 576pt |
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Height | 432pt |