The Gamma Mixture Distribution

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), ...)

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.

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.

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 \(b=n/m\)).

See also

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

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
#> Univariate Gamma mixture
#> Mixture Components:
#>   rob  inf 
#> w  0.3  0.7
#> a 20.0 50.0
#> b  4.0 10.0
# or explicitly
print(gmix)
#> Univariate Gamma mixture
#> Mixture Components:
#>   rob  inf 
#> w  0.3  0.7
#> a 20.0 50.0
#> b  4.0 10.0

# summaries are defined
summary(gmix)
#>      mean        sd      2.5%     50.0%     97.5% 
#> 5.0000000 0.8514693 3.4362134 4.9560695 6.8210139 

# sub-components may be extracted
# by component number
gmix[[2]]
#> Univariate Gamma mixture
#> Mixture Components:
#>   inf 
#> w  0.7
#> a 50.0
#> b 10.0
# or component name
gmix[["inf"]]
#> Univariate Gamma mixture
#> Mixture Components:
#>   inf 
#> w  0.7
#> a 50.0
#> b 10.0

# 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))