File:Student_t_pdf.svg
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![File:Student t pdf.svg](http://upload.wikimedia.org/wikipedia/commons/thumb/4/41/Student_t_pdf.svg/360px-Student_t_pdf.svg.png)
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Summary
DescriptionStudent t pdf.svg |
English: Plot of the density function for several members of the Student t family. |
Date | |
Source | Own work |
Author | Skbkekas |
SVG development InfoField | ![]() This plot was created with Matplotlib. |
Source code InfoField | 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")
|
Licensing
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22 February 2010
File history
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 05:45, 21 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. |
15:36, 4 March 2010 | ![]() | 360 × 288 (30 KB) | Skbkekas | Last file was incorrectly uploaded as cdf. | |
15:35, 4 March 2010 | ![]() | 360 × 288 (27 KB) | Skbkekas | Changed df's to give better spacing, used thinner lines. | |
04:08, 23 February 2010 | ![]() | 360 × 288 (32 KB) | Skbkekas | {{Information |Description={{en|1=Plot of the density function for several members of the Student t family.}} |Source={{own}} |Author=Skbkekas |Date=2010-02-22 |Permission= |other_versions= }} [[Category:Statistical charts and diagrams] |
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