gamlssMX: Function to fit finite mixture of gamlss family distributions
In gamlss.mx: Fitting Mixture Distributions with GAMLSS

Description Usage Arguments Author(s) References See Also Examples

The function gamlssMX is design for fitting a K fold non parametric mixture of gamlss family distributions.

gamlssMX(formula = formula(data), pi.formula = ~1, 
         family = "NO", weights, K = 2, prob = NULL, 
         data, control = MX.control(...), 
         g.control = gamlss.control(trace = FALSE, ...), 
         zero.component = FALSE,   ...)
gamlssMXfits(n = 5, formula = formula(data), pi.formula = ~1, 
         family = "NO", weights, K = 2, prob = NULL, 
         data, control = MX.control(), 
         g.control = gamlss.control(trace = FALSE),
         zero.component = FALSE, ... )

`formula`	This argument it should be a formula (or a list of formulea of length K) for modelling the `mu` parameter of the model. Note that modelling the rest of the distributional parameters it can be done by using the usual `...` which passes the arguments to `gamlss()`
`pi.formula`	This should be a formula for modelling the prior probabilities as a function of explanatory variables. Note that no smoothing of other additive terms are allowed here only the usual linear terms. The modelling here is done using the `multinom()` function from package `nnet`
`family`	This should be a `gamlss.family` distribution (or a list of distributions). Note that if different distributions are used here their parameters should be comparable for ease of interpretation.
`weights`	prior weights if needed
`K`	the number of finite mixtures with default `K=2`
`prob`	prior probabilities if required for starting values
`data`	the data frame nedded for the fit. Note that this is compulsory if `pi.formula` is used.
`control`	This argument sets the control parameters for the EM iterations algorithm. The default setting are given in the `MX.control` function
`g.control`	This argument can be used to pass to `gamlss()` control parameters, as in `gamlss.control`
`n`	the number of fits required in `gamlssMXfits()`
`zero.component`	whether zero component models exist, default is `FALSE`
`...`	for extra arguments

Mikis Stasinopoulos and Bob Rigby

Rigby, R. A. and Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), Appl. Statist., 54, part 3, pp 507-554.

Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.

Stasinopoulos D. M. Rigby R.A. (2007) Generalized additive models for location scale and shape (GAMLSS) in R. Journal of Statistical Software, Vol. 23, Issue 7, Dec 2007, https://www.jstatsoft.org/v23/i07/.

Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.

(see also https://www.gamlss.com/).

gamlss, gamlss.family

library(MASS)
data(geyser)
# fitting 2 finite normal mixtures 
m1<-gamlssMX(waiting~1,data=geyser,family=NO, K=2)

#fitting 2 finite gamma mixtures 
m2<-gamlssMX(waiting~1,data=geyser,family=GA, K=2)
# fitting a model for pi
# first create a data frame
geyser1<-matrix(0,ncol=2, nrow=298)
geyser1[,1] <-geyser$waiting[-1]
geyser1[,2] <-geyser$duration[-299]
colnames(geyser1)<- c("waiting", "duration")
geyser1 <-data.frame(geyser1)
# get the best of 5 fits
m3<-gamlssMXfits(n=5, waiting~1, pi.formula=~duration, data=geyser1,family=NO, K=2)
m3