gen.trun: Generates a Truncate Distribution from a gamlss.family In gamlss.tr: Generating and fitting truncated (gamlss.family) distributions

Description

The `gen.trun()` function allows the user to generate the `d`, the `p`, the `q`, the `r` and the `gamlss` fitting functions of a truncated distribution given that the input `family` is a current GAMLSS family distribution.

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).

Usage

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

Arguments

 `par` a vector with one (for `left` or `right` truncation) or two elements for `both` `family` a `gamlss.family` 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 `gamlss.family`. Functions such as BI() (binomial) produce a family object. `name` the characters you want to add to the name of new truncated distribution, by default adds `tr` `type` whether `left`, `right` or in `both` sides truncation is required `...` for extra arguments

Value

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

Author(s)

Mikis Stasinopoulos [email protected] and Bob Rigby [email protected]

References

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 http://www.gamlss.com/).

`trun.d`, `trun.p`, `trun.q`, `trun.r`
 ```1 2 3 4 5 6``` ```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) plot(function(x) pTF0to100(x, mu=80 ,sigma=20, nu=5), 0, 100) plot(function(x) qTF0to100(x, mu=80 ,sigma=20, nu=5), 0.01, .999) hist(s1<-rTF0to100(1000, mu=80 ,sigma=20, nu=5)) m1<-gamlss(s1~1, family=TF0to100) ```