mixgamma: 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 gammaMix
print(x, ...)
# S3 method for gammaPoissonMix
print(x, ...)
# S3 method for gammaExpMix
print(x, ...)
# S3 method for gammaMix
summary(object, probs = c(0.025, 0.5, 0.975), ...)
# S3 method for gammaPoissonMix
summary(object, probs = c(0.025, 0.5, 0.975), ...)

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.

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 \(b=n/m\)).

Examples

Run this code

# 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))