File:Normal Distribution PDF.svg

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Summary

Description

A selection of Normal Distribution Probability Density Functions (PDFs). Both the mean, μ, and variance, σ², are varied. The key is given on the graph.

Date

2 April 2008

Source

self-made, Mathematica, Inkscape

Author

Inductiveload

Permission
(Reusing this file)

I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

SVG development

The source code of this SVG is invalid due to an error.

This W3C-invalid chart was created with R.

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Source code

R code

Plot[
 {
  PDF[NormalDistribution[1, Sqrt[2]], x],
  PDF[NormalDistribution[2, 1], x],
  PDF[NormalDistribution[3, Sqrt[3]], x],
    },
 {x, -5, 5},
 PlotRange -> All,
 Axes -> False]

Data

#			Normal Distribution PDF
#range
x=seq(-5,5,length=200)
#plot each curve
plot(x,dnorm(x,mean=0,sd=sqrt(.2)),type="l",lwd=2,col="blue",main='Normal Distribution PDF',xlim=c(-5,5),ylim=c(0,1),xlab='X',
ylab='φμ, σ²(X)')
curve(dnorm(x,mean=0,sd=1), add=TRUE,type="l",lwd=2,col="red")
curve(dnorm(x,mean=0,sd=sqrt(5)), add=TRUE,type="l",lwd=2,col="brown")
curve(dnorm(x,mean=-2,sd=sqrt(.5)), add=TRUE,type="l",lwd=2,col="green")

Text

#                    Normal Distribution
import numpy as np
import matplotlib.pyplot as plt 

def make_gauss(N, sig, mu):
    return lambda x: N/(sig * (2*np.pi)**.5) * np.e ** (-(x-mu)**2/(2 * sig**2))

def main():
    ax = plt.figure().add_subplot(1,1,1)
    x = np.arange(-5, 5, 0.01)
    s = np.sqrt([0.2, 1, 5, 0.5])
    m = [0, 0, 0, -2] 
    c = ['b','r','y','g']

    for sig, mu, color in zip(s, m, c): 
        gauss = make_gauss(1, sig, mu)(x)
        ax.plot(x, gauss, color, linewidth=2)

    plt.xlim(-5, 5)
    plt.ylim(0, 1)
    plt.legend(['0.2', '1.0', '5.0', '0.5'], loc='best')
    plt.show()

if __name__ == '__main__':
   main()

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Thumbnail	Dimensions	User	Comment
current	16:06, 29 April 2016		720 × 460 (63 KB)	Rayhem	Lighten background grid
	17:19, 22 September 2009		720 × 460 (65 KB)	Stpasha	Trying again, there seems to be a bug with previous upload…
	17:15, 22 September 2009		720 × 460 (65 KB)	Stpasha	Curves are more distinguishable; numbers correctly rendered in roman style instead of italic
	14:07, 27 June 2009		720 × 460 (55 KB)	Autiwa	fichier environ 2 fois moins gros. Purgé des définitions inutiles, et avec des plots optimisés au niveau du nombre de points.
	18:22, 5 September 2008		720 × 460 (109 KB)	PatríciaR	from http://tools.wikimedia.pl/~beau/imgs/ (recovering lost file)
	19:09, 2 April 2008	No thumbnail	(109 KB)	Inductiveload	{{Information \|Description=A selection of Normal Distribution Probability Density Functions (PDFs). Both the mean, ''μ'', and variance, ''σ²'', are varied. The key is given on the graph. \|Source=self-made, Mathematica, Inkscape \|Date=02/04/2008 \|Author