Difference between revisions of "Beta distributions"
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=Beta distributions= | =Beta distributions= | ||
| − | For details on the beta distribution see [[WikiPedia:Beta distribution]]. | + | 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 [http://en.wikipedia.org/wiki/Beta_distribution#Shapes shapes] depending on the parameters. Their flexibility makes them useful for modelling | Beta distributions have many [http://en.wikipedia.org/wiki/Beta_distribution#Shapes shapes] depending on the parameters. Their flexibility makes them useful for modelling | ||
Revision as of 21:35, 2 August 2006
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;
?beta # or help(beta) ?rbeta # or help(rbeta) |
Usage examples are provided at;
example(beta) example(rbeta) example(dbeta) example(pbeta) example(qbeta) |
R code example 1
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, main=paste("p=",p, ", q=", q, sep="")) lines(density(x, adjust=0.4), col="red")
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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
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)
}
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