# mixbeta: Beta Mixture Density In RBesT: R Bayesian Evidence Synthesis Tools

## Description

The Beta mixture density and auxilary functions.

## Usage

  1 2 3 4 5 6 7 8 9 10 11 mixbeta(..., param = c("ab", "ms", "mn")) ms2beta(m, s, drop = TRUE) mn2beta(m, n, drop = TRUE) ## 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. object Beta mixture object. probs Quantiles reported by the summary function.

## 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=√{\frac{m(1-m)}{1+n}}, where n=a+b is the number of observations. Note that s must be less than √{m(1-m)}.

mn

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

## 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.

Other mixdist: mixcombine(), mixgamma(), mixnorm(), mix, plot.mix()
  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ## 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 print(bm4)