# File:T distribution 30df enhanced.svg

Original file(SVG file, nominally 360 × 360 pixels, file size: 67 KB)

## Summary

Description
English: Student's t-distribution with 30 degrees of freedom. Enhanced imaging
Date
Source Own work
Author IkamusumeFan
SVG development
 This diagram was created with Matplotlib.
 The file size of this SVG diagram may be irrationally large because its text has been converted to paths.

Plot using Python Matplotlib.

## Licensing

I, the copyright holder of this work, hereby publish it under the following license:

## Python (Matplotlib)

```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 previous Student's t-distributions
nu = 30	# freedom degree = 30
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)

# 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
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)

# 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")
```

## File history

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Date/TimeThumbnailDimensionsUserComment
current09:10, 29 April 2016360 × 360 (67 KB)IkamusumeFan (talk | contribs)revise based on discussions
04:55, 21 July 2013360 × 360 (86 KB)IkamusumeFan (talk | contribs)The previous edition is wrong on the degrees of freedom.
04:26, 21 July 2013360 × 360 (86 KB)IkamusumeFan (talk | contribs)Thicker lines for visibility.
04:16, 21 July 2013360 × 360 (86 KB)IkamusumeFan (talk | contribs)User created page with UploadWizard
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