Beta distributions
Contents
Beta distributions
For details on the beta distribution see WikiPedia:Beta distribution. The parameters p, and q are α & β in the Wikipedia article formula. The x axis range is from 0 to 1, the range for probabilities
Beta distributions have many shapes depending on the parameters. Their flexibility makes them useful for modelling uniform distributions β(1,1) right through to symmetric or skewed distributions, or even U shaped distributions.
R programming language
For help on functions which create/manipulate beta distributions see; <R>
?beta # or help(beta) ?rbeta # or help(rbeta)
</R> Usage examples are provided at; <R>
example(beta) example(rbeta) example(dbeta) example(pbeta) example(qbeta)
</R>
R code example 1
Let's generate a beta distribution using the rbeta built in R function. <R>
quartz() # Alter the parameters n <- 1000 # Number of observations p <- 0.1 q <- 0.1
x <- rbeta(n, shape1= p, shape2=q)
breaks <- seq(0,1, length=21)
hist(x, breaks=breaks, freq=FALSE, main=paste("p=",p, ", q=", q, sep="")) lines(density(x, adjust=0.4), col="red")
</R> Notice α and β are less than one, so the plot is U shaped, as described in Wikipedia:Beta distribution#Shapes.
Symmetry of α Β
R code example 2
<R>
quartz()
# Alter the parameters
n <- 10000 # Number of observations
for(i in 1:50) {
p <- q <- i
x <- rbeta(n, shape1= p, shape2=q)
breaks <- seq(0,1, length=21)
hist(x, breaks=breaks, freq=FALSE, main=paste("p=",p, ", q=", q, sep=""))
lines(density(x, adjust=0.4), col="red")
Sys.sleep(1)
}
</R>>
