File:Student t pdf.svg
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Original file (SVG file, nominally 360 × 288 pixels, file size: 39 KB)
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This is a file from the Wikimedia Commons. The description on its description page there is shown below.
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Summary
| Description |
English: Plot of the density function for several members of the Student t family. |
| Date | |
| Source | Own work |
| Author | Skbkekas |
| SVG development |  This plot was created with Matplotlib. |
| Source code | Python code# Origin: Skbkekas
# Enhanced: Ika, 2013-07-24
import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
col = ['orange', 'purple', 'deepskyblue']
X = np.arange(-5, 5, 0.001)
plt.clf()
plt.figure(figsize=(4,3.2))
plt.axes([0.17,0.13,0.79,0.8])
plt.hold(True)
A = []
for k,nu in enumerate([1,2,5]):
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)
a = plt.plot(X, np.exp(Y), '-', color=col[k], lw=1.5)
A.append(a[0])
# Draw the curve of Normal distribution, which is the limit of t-distribution sequence.
mu = 0 # mean = 0
sigma = 1 # variance = 1
M = 1/(sigma*np.sqrt(2*np.pi))
N = np.exp(-(X-mu)*(X-mu)/(2*sigma*sigma));
Y = M*N
a = plt.plot(X, Y, '-', color='black', lw=1.5)
A.append(a[0])
plt.xlabel("x")
plt.ylabel("P(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="upper right")
bx.draw_frame(False)
plt.xlim(-5,5)
plt.savefig("student_t_pdf.pdf")
plt.savefig("student_t_pdf.svg")
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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 | Dimensions | User | Comment | |
|---|---|---|---|---|
| current | 22:45, 20 July 2013 | 360 × 288 (39 KB) | IkamusumeFan | 1. Using \nu instead of df; 2. The previous edition used 1000 to stand for infinity case. The limit of the t-distribution sequence is normal distribution. Thus, we use normal distribution instead. |
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