File:Student t cdf.svg
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Size of this PNG preview of this SVG file: 360 × 288 pixels. Other resolutions: 300 × 240 pixels | 600 × 480 pixels | 960 × 768 pixels | 1,280 × 1,024 pixels | 2,560 × 2,048 pixels.
Original file (SVG file, nominally 360 × 288 pixels, file size: 35 KB)
Summary
| Description |
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 |  This plot was created with Matplotlib. |
| Source code | 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
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.
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:37, 3 April 2014 | | 360 × 288 (35 KB) | commons>Hydrox | fixed colours (hand-edited SVG) |
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