mixgamma: The Gamma Mixture Distribution

In RBesT: R Bayesian Evidence Synthesis Tools

The Gamma Mixture Distribution

Description

The gamma mixture density and auxiliary functions.

Usage

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'
print(x, ...)

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

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

## 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.
x	The mixture to print
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=\sqrt{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 \cdot 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.

See Also

Other mixdist: mix, mixbeta(), mixcombine(), mixjson, mixmvnorm(), mixnorm(), mixplot

Examples

# 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))

RBesT documentation built on June 8, 2025, 10:05 a.m.