Image:Normal approximation to binomial.svg

[edit] Summary

svg version of the same png Normal_approximation_to_binomial.png file. Original author: User:MarkSweep Created with gnuplot.

Cleanup: red lines cross blue line.

gnuplot source under GPL:

# normal (Gaussian) distribution
_ln_dnorm(x, m, s) = -0.5 * log(2*pi) - log(s) - 0.5*((x-m)*1.0/s)**2
dnorm(x, mean, sd) = exp(_ln_dnorm(x, mean, sd))
pnorm(x, mean, sd) = norm((x-mean) * 1.0/sd)

# binomial distribution
_ln_binom(x, n, p) =\
 lgamma(n+1) - lgamma(x+1) - lgamma(n-x+1) + x*log(p) + (n-x)*log(1-p)
dbinom(x, size, prob) = (x==int(x))? exp(_ln_binom(floor(x), size,  prob)) : 0
pbinom(x, size, prob) =\
 (x<0)? 0 : (x<size)? ibeta(size-floor(x), floor(x)+1, 1-prob) : 1

set terminal svg
set output "Normal approximation to binomial.svg"

set key 22,0.13

n = 48
p = 0.25
xmax = 25

set samples 50*xmax+1

plot [0:xmax] \
    dbinom(x, n, p) with impulses title "Binom(48, 0.25)", \
    dnorm(x, n*p, sqrt(n*p*(1-p))) linetype 3 title "Norm(12, 3)"

[edit] Licensing

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation license, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled "GNU Free Documentation license". Aragonés | العربية | Asturianu | Български | বাংলা | ইমার ঠার/বিষ্ণুপ্রিয়া মণিপুরী | Brezhoneg | Bosanski | Català | Cebuano | Česky | Dansk | Deutsch | Ελληνικά | English | Esperanto | Español | Eesti | Euskara | فارسی | Suomi | Français | Gaeilge | Galego | עברית | Hrvatski | Magyar | Bahasa Indonesia | Ido | Íslenska | Italiano | 日本語 | ქართული | ភាសាខ្មែរ | 한국어 | Kurdî / كوردی | Latina | Lëtzebuergesch | Lietuvių | Bahasa Melayu | Nnapulitano | Nederlands | ‪Norsk (nynorsk)‬ | ‪Norsk (bokmål)‬ | Occitan | Polski | Português | Română | Русский | Slovenčina | Slovenščina | Shqip | Српски / Srpski | Svenska | తెలుగు | ไทย | Türkçe | Українська | اردو | Tiếng Việt | Volapük | Yorùbá | ‪中文(中国大陆)‬ | ‪中文(台灣)‬ | +/-

• Normal distribution