In a gamma mixture model, we can assume that the shapes are equal in each/all cluster(s) or not. We can also assume that the scales are equal in each/all cluster(s) or not.
check if a vector of gamma mixture model name is correct.
1 2 3 4 5  clusterGammaNames(prop = "all", shapeInCluster = "all",
shapeBetweenCluster = "all", scaleInCluster = "all",
scaleBetweenCluster = "all")
clusterValidGammaNames(names)

prop 
A character string equal to "equal", "free" or "all". Default is "all". 
shapeInCluster 
A character string equal to "equal", "free" or "all". Default is "all". 
shapeBetweenCluster 
A character string equal to "equal", "free" or "all". Default is "all". 
scaleInCluster 
A character string equal to "equal", "free" or "all". Default is "all". 
scaleBetweenCluster 
A character string equal to "equal", "free" or "all". Default is "all". 
names 
a vector of character 
Some configuration are impossibles. If the shapes are equal between all the clusters, then the scales cannot be equal between all the clusters. Conversely if the scales are equal between all the cluster, then the shapes cannot be equal between all the clusters.
This gives rise to 24 models:
The proportions can be equal or free.
The shapes can be equal or free in each clusters.
The shapes can be equal or free between all clusters.
The scales can be equal or free for each clusters.
The scales can be equal or free between all clusters.
The model names are summarized in the following array:
& ajk & ak & aj & a 
bjk & gamma_*_ajk_bjk & gamma_*_ak_bjk & gamma_*_aj_bjk & gamma_*_a_bjk 
bk & gamma_*_ajk_bk & gamma_*_ak_bk & gamma_*_aj_bk & gamma_*_a_bk 
bj & gamma_*_ajk_bj & gamma_*_ak_bj & NA & NA 
b & gamma_*_ajk_b & gamma_*_ak_b & NA & NA 
A vector of character with the model names.
1 2 3  clusterGammaNames()
## same as c("gamma_p_ak_bj", "gamma_pk_ak_bj")
clusterGammaNames("all", "equal", "free", "free", "equal")

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