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Summary

Description
English: Student's t-distribution with 5 degrees of freedom. Enhanced plotting.
Date
Source Own work
Author IkamusumeFan
SVG development
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Source code
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Python code

import numpy as np
import matplotlib.pyplot as plt
import scipy.special as sp
 
X = np.arange(-4, 4, 0.01)	# range of the graph                                                                            
 
plt.clf()
plt.figure(figsize=(4,4))
plt.axes([0.17,0.13,0.79,0.8])
plt.hold(True)

Q = []	# No curves at first.

# Draw the curve of Normal distribution
mu = 0	# mean = 0
sigma = 1	# variance = 1
A = 1/(sigma*np.sqrt(2*np.pi))
B = np.exp(-(X-mu)*(X-mu)/(2*sigma*sigma));
Y = A*B
a = plt.plot(X, Y, '-', color='blue', lw=2)
Q.append(a)

# Draw the curve of Student's t-distribution
mu = 0	# mean = 0
nu = 5	# freedom degree = 5
A = np.exp(sp.gammaln((nu+1)/2.0));
B = np.exp(sp.gammaln(nu/2.0))*np.sqrt(nu*np.pi);
C = (1+X*X/nu)**(-(nu+1)/2.0);
Y = A*C/B;
a = plt.plot(X, Y, '-', color='red', lw=2)
Q.append(a)

# Draw the previous Student's t-distributions
for previous_nu in range(1,nu):
	mu = 0	# mean = 0
	A = np.exp(sp.gammaln((previous_nu+1)/2.0));
	B = np.exp(sp.gammaln(previous_nu/2.0))*np.sqrt(previous_nu*np.pi);
	C = (1+X*X/previous_nu)**(-(previous_nu+1)/2.0);
	Y = A*C/B;
	a = plt.plot(X, Y, '-', color='green', lw=1)
	Q.append(a)

# Remaining steps to finish drawing the graph. 
plt.xlabel("x")
plt.ylabel("P(x)")
plt.xlim(-4,4)

# Saving the output.
plt.savefig("T_distribution_1df.pdf")
plt.savefig("T_distribution_1df.eps")
plt.savefig("T_distribution_1df.svg")

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 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.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

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20 July 2013

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Date/TimeThumbnailDimensionsUserComment
current04:45, 21 July 2013Thumbnail for version as of 04:45, 21 July 2013360 × 360 (35 KB)IkamusumeFanThe previous edition is incorrect on the degrees of freedom.
04:04, 21 July 2013Thumbnail for version as of 04:04, 21 July 2013360 × 360 (35 KB)IkamusumeFanUser created page with UploadWizard

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