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gen.trun {}

Generates a truncated distribution from a


The gen.trun() function allows the user to generate d, p, q, and r distribution functions plus an extra function for fitting a truncated distribution with gamlss.

For continuous distributions left truncation at 3 means that the random variable can take the value 3. For discrete distributions left truncation at 3 means that the random variable can take values from 4 onwards. This is the same for right truncation. Truncation at 15 for a discrete variable means that 15 and greater values are not allowed but for continuous variable it mean values greater that 15 are not allowed (so 15 is a possible value).

If the user want a different link (rather the default) for any of the parameters she/he has to declare at the generation of the functions, see example.


gen.trun(par = c(0), family = "NO", name = "tr", 
         type = c("left", "right", "both"), 
         varying = FALSE,...)


a vector with one (for "left" or "right" truncation) or two elements for "both". When the argument varying = TRUE then par can be a vector or a matrix with two columns respectively.
a object, which is used to define the distribution and the link functions of the various parameters. The distribution families supported by gamlss() can be found in
the extra characters to be added to the name of new truncated distribution, by default it adds tr
whether "left", "right" or in "both" sides truncation is required
whether the truncation varies for different observations. This can be useful in regression analysis. If varying = TRUE then par should be an n-length vector for type equal "left" and "right" and an n by 2 matrix for type="both"
for extra arguments


Returns the d, the p, the q, the r and the fitting functions of a truncated distribution.


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.

Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2003) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also

See Also

trun.d, trun.p, trun.q, trun.r


# generating a t-distribution from 0 to 100      
gen.trun(par=c(0,100),family="TF", name="0to100", type="both")
plot(function(x) dTF0to100(x, mu=80 ,sigma=20, nu=5), 0, 100, ylab="pdf")
plot(function(x) pTF0to100(x, mu=80 ,sigma=20, nu=5), 0, 100, ylab="cdf")
plot(function(x) qTF0to100(x, mu=80 ,sigma=20, nu=5), 0.01, .999, ylab="invcdf")
hist(s1<-rTF0to100(1000, mu=80 ,sigma=20, nu=5), ylab="hist", xlab="x", 
            main="generated data")
m1<-histDist(s1, family=TF0to100, xlim=c(0,100))# fitting the data
# using the argumnt varying 
# left part varies right part equal 100
leftPAR <- rPO(100)
gen.trun(par=cbind(leftPAR,rep(100, 100)),family="TF", name="0to100Varying", 
            type="both", varying=TRUE)
YY<- rTF0to100Varying(100, mu=80, sigma=20, nu=5)
m1<-gamlss(YY~1, family=TF0to100Varying)
# generating with different link
gen.trun(0, NO(


Mikis Stasinopoulos and Bob Rigby

Documentation reproduced from package, version 4.3-1. License: GPL-2 | GPL-3