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File:Binomial versus poisson.svg

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    Summary

    Description
    English: Comparison of the Poisson distribution (black dots) and the binomial distribution with n=10 (red line), n=20 (blue line), n=1000 (green dots). All distributions have a mean of 5.
    Source Code
    svg("poisson-vs-binomial.svg", width=4, height=4)
x <- 0:10
pmean <- 5
pal <- c("black", "tomato", "royalblue", "darkgreen")
par0 <- par(mar=c(4,4,0.5,0)+0.5)
plot.new(); plot.window(range(x), c(0,max(dbinom(x, 10, pmean/10))))
axis(1); axis(2); title(xlab=expression(k), ylab=expression(Density(k)))
abline(h=0, lwd=0.1)
lines(x, dpois(x, pmean), type="h", lwd=2, col=pal[[1]])
for (i in 1:3) {
  n <- c(10, 20, 1000)[[i]]
  y <- dbinom(x, n, pmean/n)
  lines(x, y, type="b", col=pal[[i+1]], pch=NA, lty=3, lwd=0.5)
  points(x, y, col=pal[[i+1]], lwd=2)
}
legend("topright", expression(Poisson(lambda==5),
    Binom(n==10),Binom(n==20),Binom(n==1000)),
  lwd=2, lty=c(1,NA,NA,NA), pch=c(NA,1,1,1), col=pal, cex=0.6)
par(par0)
dev.off()
    Date
    Source Own work
    Author Sergio01
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    GNU head 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.
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    inception

    22 April 2010

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    checksum

    730f5a09e8b3340bafaa2ff7a629224c86add6e3

    determination method or standard: SHA-1

    data size

    64,151 byte

    height

    360 pixel

    width

    360 pixel

    File history

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    Date/TimeThumbnailDimensionsUserComment
    current15:46, 1 July 2012Thumbnail for version as of 15:46, 1 July 2012360 × 360 (63 KB)Smason79updated version with more obvious symbols and better layout for viewing in thumbnail (sorry for the revert noise, didn't realise how it would work!)
    15:39, 1 July 2012Thumbnail for version as of 15:39, 1 July 2012694 × 694 (48 KB)Smason79Reverted to version as of 19:47, 22 April 2010; wikipedia rendering not like mine, about to fix
    15:37, 1 July 2012Thumbnail for version as of 15:37, 1 July 2012540 × 540 (61 KB)Smason79both distributions are discrete; the previous version showed them smoothed out as if they were continuous
    19:47, 22 April 2010Thumbnail for version as of 19:47, 22 April 2010694 × 694 (48 KB)Sergio01{{Information |Description={{en|1=Comparison the Poisson distribution (black dots) and the binomial distribution with n=10 (red line), n=20 (blue line), n=1000 (green dots). All distributions have a mean of 5.}} |Source={{own}} |Author=[[User:Sergio01|Ser

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