Difference between revisions of "Beta distributions"
m (Caretaker: categories) |
(Use GeSHi <R> tags) |
||
| Line 9: | Line 9: | ||
== R programming language == | == R programming language == | ||
For help on functions which create/manipulate beta distributions see; | For help on functions which create/manipulate beta distributions see; | ||
| − | < | + | <R> |
?beta # or help(beta) | ?beta # or help(beta) | ||
?rbeta # or help(rbeta) | ?rbeta # or help(rbeta) | ||
| − | </ | + | </R> |
Usage examples are provided at; | Usage examples are provided at; | ||
| − | < | + | <R> |
example(beta) | example(beta) | ||
example(rbeta) | example(rbeta) | ||
| Line 20: | Line 20: | ||
example(pbeta) | example(pbeta) | ||
example(qbeta) | example(qbeta) | ||
| − | </ | + | </R> |
== R code example 1 == | == R code example 1 == | ||
| + | |||
Lets generate a beta distribution using the ''rbeta'' built in R function. | Lets generate a beta distribution using the ''rbeta'' built in R function. | ||
| − | < | + | <R> |
quartz() | quartz() | ||
# Alter the parameters | # Alter the parameters | ||
| Line 34: | Line 35: | ||
breaks <- seq(0,1, length=21) | 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") | 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|Wikipedia:Beta distribution#Shapes]]. | Notice α and β are less than one, so the plot is U shaped, as described in [[Wikipedia:Beta distribution#Shapes|Wikipedia:Beta distribution#Shapes]]. | ||
== Symmetry of α Β == | == Symmetry of α Β == | ||
==R code example 2== | ==R code example 2== | ||
| − | < | + | <R> |
quartz() | quartz() | ||
# Alter the parameters | # Alter the parameters | ||
| Line 51: | Line 52: | ||
Sys.sleep(1) | Sys.sleep(1) | ||
} | } | ||
| − | </ | + | </R>> |
== See also == | == See also == | ||
[[BetaDistributions.R]] | [[BetaDistributions.R]] | ||
Revision as of 22:50, 11 June 2007
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
Lets 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>>
