mixgamma function

The Gamma Mixture Distribution

The gamma mixture density and auxiliary functions.

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.

Returns

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 $a=m n$), for an Exp likelihood $n=a$ (and $b=n/m$).

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))

See Also

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