File:Student t cdf.svg
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Summary
[edit]DescriptionStudent t cdf.svg |
English: Plot of the cumulative distribution functions of several members of the Student t-family of probability distributions. |
Date | |
Source | Own work |
Author | Skbkekas |
SVG development InfoField | This plot was created with Matplotlib. |
Source code InfoField | Python codeimport numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
import scipy.integrate as integral
col = ['orange', 'purple', 'deepskyblue']
X = np.arange(-5, 5, 0.005)
plt.clf()
plt.figure(figsize=(4,3.2))
plt.axes([0.17,0.13,0.79,0.8])
plt.hold(True)
A = []
def PDF(x,nu):
Y = -(nu+1)*np.log(1+x**2/nu)/2
Y += sp.gammaln((nu+1)/2.0)
Y -= sp.gammaln(nu/2.0)
Y -= 0.5*np.log(nu*np.pi)
Y = np.exp(Y)
return Y
for k,nu in enumerate([1,2,5]):
Y=[]
for x in X:
Y.append(integral.quad(lambda t: PDF(t,nu),-1000,x))
a = plt.plot(X, Y, '-', color=col[k], lw=1.5)
A.append(a)
# Degenerate into Normal distribution
from scipy.stats import norm
Y = norm.cdf(X)
a = plt.plot(X, Y, '-', color='black', lw=1.5)
A.append(a)
plt.xlabel("x")
plt.ylabel(u"P(X\N{Less-THAN OR EQUAL TO}x)")
bx = plt.legend(A, (r"$\nu=1$", r"$\nu=2$", r"$\nu=5$", r"$\nu=+\infty$"),\
numpoints=1, handlelen=0.05, handletextpad=0.4,\
loc="lower right")
bx.draw_frame(False)
plt.xlim(-5,5)
plt.savefig("student_t_cdf.pdf")
plt.savefig("student_t_cdf.eps")
plt.savefig("student_t_cdf.svg")
|
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is licensed under the Creative Commons Attribution 3.0 Unported 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.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 23:37, 3 April 2014 | 360 × 288 (35 KB) | Hydrox (talk | contribs) | fixed colours (hand-edited SVG) | |
07:58, 21 July 2013 | 360 × 288 (35 KB) | IkamusumeFan (talk | contribs) | Adjust the axis for better display. | ||
07:51, 21 July 2013 | 360 × 288 (35 KB) | IkamusumeFan (talk | contribs) | 1. Using \nu instead of df, which appears in Scipy's documentation; 2. Since for some operating systems and Python versions, Scipy's stdtr function has visible errors around t=+1 and -1, we adjust the computation of CDF according to the integral defini... | ||
15:42, 4 March 2010 | 360 × 288 (28 KB) | Skbkekas (talk | contribs) | Changed df's to give better spacing, used thinner lines. | ||
04:11, 23 February 2010 | 360 × 288 (27 KB) | Skbkekas (talk | contribs) | {{Information |Description={{en|1=Plot of the cumulative distribution functions of several members of the Student t-family of probability distributions.}} |Source={{own}} |Author=Skbkekas |Date=2010-02-22 |Permission= |other_versions= }} |
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Width | 288pt |
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Height | 230pt |