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# hilbe_NBR2_F3_1.r
# Table 3.1
# Script for creating Poisson and negative binomial (NB2) distributions
# on single graph with user specified number of observations (obs),
# mean (mu), counts (0:specified), and NB2 ancillary parameter value (alpha).
# Additional enhanced graphic can be displayed; -ggplot2- must be installed.
# From Hilbe, Negative Binomial Regression, 2nd ed, Cambridge Univ. Press
# Table 3.1; Figure 3.1
#
# ------------------------------------------
# User specified values; defaults displayed
obs <- 11
mu <- 2
y <- 0:10
alpha <- 1.5
# ------------------------------------------
amu <- mu*alpha
ynb2 = exp(
y*log(amu/(1+amu))
- (1/alpha)*log(1+amu)
+ log( gamma(y +1/alpha) )
- log( gamma(y+1) )
- log( gamma(1/alpha) )
)
xbar = "mu"
a = "alpha"
plot( y, ynb2, col="red", pch=5,
main="Poisson vs Negative Binomial PDFs")
lines( y, ynb2, col="red")
points(y, yp2, col="blue", pch=2)
lines( y, yp2, col="blue")
legend(4.3,.40,
c("Negative Binomial: mean=2, a=1.5",
"Poisson: mean=2"),
col=( c("red","blue") ),
pch=( c(5,2) ),
lty=1)
#========= FOR NICER GRAPHIC =======================
zt <- 0:10 #zt is Zero to Ten
x <- c(zt,zt) #two zt's stacked for use with ggplot2
newY <- c(yp2, ynb2) #Now stacking these two vars
Distribution <- gl(n=2,k=11,length=22,
label=c("Poisson","Negative Binomial")
)
NBPlines <- data.frame(x,newY,Distribution)
library("ggplot2")
ggplot( NBPlines, aes(x,newY,shape=Distribution,col=Distribution ) ) +
geom_line() + geom_point()
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