Beta distributions
From Organic Design wiki
Beta distributions
For details on the beta distribution see WikiPedia:Beta distribution. Notice that thee distribution is symmetric for the parameters p, and q (α & β in the Wikipedia article formula), and that the x axis range is from 0 to 1, a probability.
Beta distributions have many shapes depending on the parameters. Their flexibility makes them useful for modelling uniform distributions &Beta(1,1) right through to symmetric or skewed distributions.
R programming language
For help on functions which create/manipulate beta distributions see;
|
?beta # or help(beta) ?rbeta # or help(rbeta) |
Usage examples are provided at;
example(beta) example(rbeta) example(dbeta) example(pbeta) example(qbeta) |
Lets generate a beta distribution using the rbeta built in R function.
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) lines(density(x, adjust=0.4), col="red") |
Symmetry of α Β
quartz()
# Alter the parameters
n <- 1000 # 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")
}
