File:Student t cdf.svg

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English: Plot of the cumulative distribution functions of several members of the Student t-family of probability distributions.
Date
Source Own work
Author Skbkekas
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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 import scipy.integrate as integral   col = ['orange', 'purple', 'deepskyblue']   X = np.arange(-5, 5, 0.005)   plt.clf() plt.figure(figsize=(4,3.2)) plt.axes([0.17,0.13,0.79,0.8]) plt.hold(True)   A = []  def PDF(x,nu): 	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) 	Y = np.exp(Y) 	return Y  for k,nu in enumerate([1,2,5]): 	Y=[] 	for x in X: 		Y.append(integral.quad(lambda t: PDF(t,nu),-1000,x)) 	a = plt.plot(X, Y, '-', color=col[k], lw=1.5) 	A.append(a)  # Degenerate into Normal distribution from scipy.stats import norm Y = norm.cdf(X) a = plt.plot(X, Y, '-', color='black', lw=1.5) A.append(a)   plt.xlabel("x") plt.ylabel(u"P(X\N{Less-THAN OR EQUAL TO}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="lower right") bx.draw_frame(False) plt.xlim(-5,5)   plt.savefig("student_t_cdf.pdf") plt.savefig("student_t_cdf.eps") plt.savefig("student_t_cdf.svg")

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22 February 2010

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Date/TimeThumbnailDimensionsUserComment
current23:37, 3 April 2014Thumbnail for version as of 23:37, 3 April 2014360 × 288 (35 KB)Hydroxfixed colours (hand-edited SVG)
07:58, 21 July 2013Thumbnail for version as of 07:58, 21 July 2013360 × 288 (35 KB)IkamusumeFanAdjust the axis for better display.
07:51, 21 July 2013Thumbnail for version as of 07:51, 21 July 2013360 × 288 (35 KB)IkamusumeFan1. Using \nu instead of df, which appears in Scipy's documentation; 2. Since for some operating systems and Python versions, Scipy's stdtr function has visible errors around t=+1 and -1, we adjust the computation of CDF according to the integral defini...
15:42, 4 March 2010Thumbnail for version as of 15:42, 4 March 2010360 × 288 (28 KB)SkbkekasChanged df's to give better spacing, used thinner lines.
04:11, 23 February 2010Thumbnail for version as of 04:11, 23 February 2010360 × 288 (27 KB)Skbkekas{{Information |Description={{en|1=Plot of the cumulative distribution functions of several members of the Student t-family of probability distributions.}} |Source={{own}} |Author=Skbkekas |Date=2010-02-22 |Permission= |other_versions= }}

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