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The R package gamlss.dist contains more than 100 distributions. We are refer to those distributions as “” distributions a name also given to the equivalent R objects. Each of those “” distributions has five related functions:

  •  the probability density function (d)
  • the cumulative distribution function (p)
  • the inverse of the cumulative distribution function and (q)
  • a function which generates random numbers from the distribution  (r) and
  • the fitting gamlss function (what the gamlss() function uses for fitting)
The type of distribution to use depends on the type of the response variable. Within the there are three distinct types of distributions:
  1.  continuous distributions
  2. discrete distributions
  3. mixed distributions 

More details about the available distributions can be found in the draft version of the the book `Distributions for Modelling Location, Scale and Shape: Using GAMLSS in R’.

In addition any distribution can be:

  • truncated  using  the function gen.trun() of the package
  • censored  using  the function gen.cens() of the package gamlss.cens 
  • finite mixed using  the package 

Also any continuous distribution defined on real line can be log or logit transformed using the function gen.Family().

Additional information on how to use mixed distributions within GAMLSS is provided by the two vignettes: