File:Student t pdf.svg
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Original file (SVG file, nominally 360 × 288 pixels, file size: 39 KB)
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")
|
Licensing
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File history
Click on a date/time to view the file as it appeared at that time.
| 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. |
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