Beta Mixture Density

The Beta mixture density and auxilary functions.

Usage

mixbeta(..., param = c("ab", "ms", "mn"))

ms2beta(m, s, drop = TRUE)

mn2beta(m, n, drop = TRUE)

# S3 method for class 'betaMix'
print(x, ...)

# S3 method for class 'betaBinomialMix'
print(x, ...)

# S3 method for class 'betaMix'
summary(object, probs = c(0.025, 0.5, 0.975), ...)

# S3 method for class 'betaBinomialMix'
summary(object, probs = c(0.025, 0.5, 0.975), ...)

Arguments

...

List of mixture components.

param

Determines how the parameters in the list are interpreted. See details.

m

Vector of means of beta mixture components.

s

Vector of standard deviations of beta mixture components.

drop

Delete the dimensions of an array which have only one level.

n

Vector of number of observations.

x

The mixture to print

object

Beta mixture object.

probs

Quantiles reported by the summary function.

Value

mixbeta returns a beta mixture with the specified mixture components. ms2beta and mn2beta return the equivalent natural a and b parametrization given parameters m, s, or n.

Details

Each entry in the ... argument list is expected to be a triplet of numbers which defines the weight \(w_k\), first and second parameter of the mixture component \(k\). A triplet can optionally be named which will be used appropriately.

The first and second parameter can be given in different parametrizations which is set by the param option:

ab

Natural parametrization of Beta density (a=shape1 and b=shape2). Default.

ms

Mean and standard deviation, \(m=a/(a+b)\) and \(s=\sqrt{\frac{m(1-m)}{1+n}}\), where \(n=a+b\) is the number of observations. Note that \(s\) must be less than \(\sqrt{m(1-m)}\).

mn

Mean and number of observations, \(n=a+b\).

See also

Other mixdist: mix, mixcombine(), mixgamma(), mixmvnorm(), mixnorm(), mixplot

Examples

## a beta mixture
bm <- mixbeta(rob=c(0.2, 2, 10), inf=c(0.4, 10, 100), inf2=c(0.4, 30, 80))

# mean/standard deviation parametrization
bm2 <- mixbeta(rob=c(0.2, 0.3, 0.2), inf=c(0.8, 0.4, 0.01), param="ms")

# mean/observations parametrization
bm3 <- mixbeta(rob=c(0.2, 0.3, 5), inf=c(0.8, 0.4, 30), param="mn")

# even mixed is possible
bm4 <- mixbeta(rob=c(0.2, mn2beta(0.3, 5)), inf=c(0.8, ms2beta(0.4, 0.1)))

# print methods are defined
bm4
#> Univariate beta mixture
#> Mixture Components:
#>   rob  inf 
#> w  0.2  0.8
#> a  1.5  9.2
#> b  3.5 13.8
print(bm4)
#> Univariate beta mixture
#> Mixture Components:
#>   rob  inf 
#> w  0.2  0.8
#> a  1.5  9.2
#> b  3.5 13.8