# mixgamma: The Gamma Mixture Distribution In RBesT: R Bayesian Evidence Synthesis Tools

## Description

The gamma mixture density and auxiliary functions.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```mixgamma(..., param = c("ab", "ms", "mn"), likelihood = c("poisson", "exp")) ms2gamma(m, s, drop = TRUE) mn2gamma(m, n, likelihood = c("poisson", "exp"), drop = TRUE) ## S3 method for class 'gammaMix' summary(object, probs = c(0.025, 0.5, 0.975), ...) ## S3 method for class 'gammaPoissonMix' 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. `likelihood` Defines with what likelihood the Gamma density is used (Poisson or Exp). Defaults to `poisson`. `m` Vector of means of the Gamma mixture components `s` Vector of standard deviations of the gamma mixture components, `drop` Delete the dimensions of an array which have only one level. `n` Vector of sample sizes of the Gamma mixture components. `object` Gamma 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 Gamma density (`a`=shape and `b`=rate). Default.

ms

Mean and standard deviation, m=a/b and s=√{a}/b.

mn

Mean and number of observations. Translation to natural parameter depends on the `likelihood` argument. For a Poisson likelihood n=b (and a=m n), for an Exp likelihood n=a (and b=n/m).

## Value

`mixgamma` returns a gamma mixture with the specified mixture components. `ms2gamma` and `mn2gamma` return the equivalent natural `a` and `b` parametrization given parameters `m`, `s`, or `n`.

Other mixdist: `mixbeta()`, `mixcombine()`, `mixnorm()`, `mix`, `plot.mix()`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```# Gamma mixture with robust and informative component gmix <- mixgamma(rob=c(0.3, 20, 4), inf=c(0.7, 50, 10)) # objects can be printed gmix # or explicitly print(gmix) # summaries are defined summary(gmix) # sub-components may be extracted # by component number gmix[[2]] # or component name gmix[["inf"]] # alternative mean and standard deviation parametrization gmsMix <- mixgamma(rob=c(0.5, 8, 0.5), inf=c(0.5, 9, 2), param="ms") # or mean and number of observations parametrization gmnMix <- mixgamma(rob=c(0.2, 2, 1), inf=c(0.8, 2, 5), param="mn") # and mixed parametrizations are also possible gfmix <- mixgamma(rob1=c(0.15, mn2gamma(2, 1)), rob2=c(0.15, ms2gamma(2, 5)), inf=c(0.7, 50, 10)) ```