Description Usage Arguments Details Value Note Author(s) References See Also Examples

This function can be used to fit truncated distributions. It takes as an argument an existing GAMLSS family distribution and
a parameter vector, of the type c(left.value, right.value), and generates a `gamlss.family`

object which then can be used to fit
a truncated distribution.

1 2 |

`par` |
a vector with one (for |

`family` |
an existing |

`type` |
what type of truncation is required, |

`name` |
a character string to be added to name of the created object i.e. with |

`local` |
if TRUE the function will try to find the environment of |

`delta` |
the delta increment used in the numerical derivatives |

`varying` |
whether the truncation varies for diferent observations. This can be usefull in regression analysis. If |

`...` |
for extra arguments |

This function is created to help the user to fit a truncated form of existing `gamlss`

distribution.
It does this by taking an existing `gamlss.family`

and changing some of the components of the distribution to help the fitting process.
It particular it i) creates a pdf (`d`

) and a cdf (`p`

) function within `gamlss`

,
ii) changes the global deviance function `G.dev.incr`

, the first derivative functions (see note below) and the quantile residual function.

It returns a `gamlss.family`

object which has all the components needed for fitting a distribution in `gamlss`

.

This function is experimental and could be changed. The function `trun`

changes
the first derivatives of the original gamlss family `d`

function to numerical derivatives
for the new truncated `d`

function. The default increment `delta`

,
for this numerical derivatives function, is `eps * pmax(abs(x), 1)`

where
`eps<-sqrt(.Machine$double.eps)`

. The default `delta`

could be inappropriate
for specific applications and can be overwritten by using the argument `delta`

.

Mikis Stasinopoulos [email protected] 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.

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.org/).

`trun.d`

, `trun.p`

, `trun.q`

, `trun.r`

, `gen.trun`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
# generate a left truncated zero t family
gen.trun(0,family="TF")
# take a random sample of 1000 observations
sam<-rTFtr(1000,mu=10,sigma=5, nu=5 )
hist(sam)
# fit the distribution to the data
mod1<-gamlss(sam~1, family=trun(0,TF))
mod1
# now create a gamlss.family object before the fitting
Ttruc.Zero<- trun(par=0,family=TF, local=FALSE)
mod2<-gamlss(sam~1, family=Ttruc.Zero)
# now check the sensitivity of delta
Ttruc.Zero<- trun(par=0,family=TF, local=FALSE, delta=c(0.01,0.01, 0.01))
mod3<-gamlss(sam~1, family=Ttruc.Zero)
``` |

```
Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data
Loading required package: nlme
Loading required package: parallel
********** GAMLSS Version 5.1-2 **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.
A truncated family of distributions from TF has been generated
and saved under the names:
dTFtr pTFtr qTFtr rTFtr TFtr
The type of truncation is left
and the truncation parameter is 0
GAMLSS-RS iteration 1: Global Deviance = 6141.149
GAMLSS-RS iteration 2: Global Deviance = 6138.934
GAMLSS-RS iteration 3: Global Deviance = 6138.416
GAMLSS-RS iteration 4: Global Deviance = 6138.318
GAMLSS-RS iteration 5: Global Deviance = 6138.301
GAMLSS-RS iteration 6: Global Deviance = 6138.297
GAMLSS-RS iteration 7: Global Deviance = 6138.296
GAMLSS-RS iteration 8: Global Deviance = 6138.295
Family: c("TFtr", "left truncated t Family")
Fitting method: RS()
Call: gamlss(formula = sam ~ 1, family = trun(0, TF))
Mu Coefficients:
(Intercept)
9.866
Sigma Coefficients:
(Intercept)
1.626
Nu Coefficients:
(Intercept)
1.645
Degrees of Freedom for the fit: 3 Residual Deg. of Freedom 997
Global Deviance: 6138.3
AIC: 6144.3
SBC: 6159.02
GAMLSS-RS iteration 1: Global Deviance = 6141.149
GAMLSS-RS iteration 2: Global Deviance = 6138.934
GAMLSS-RS iteration 3: Global Deviance = 6138.416
GAMLSS-RS iteration 4: Global Deviance = 6138.318
GAMLSS-RS iteration 5: Global Deviance = 6138.301
GAMLSS-RS iteration 6: Global Deviance = 6138.297
GAMLSS-RS iteration 7: Global Deviance = 6138.296
GAMLSS-RS iteration 8: Global Deviance = 6138.295
GAMLSS-RS iteration 1: Global Deviance = 6141.133
GAMLSS-RS iteration 2: Global Deviance = 6138.925
GAMLSS-RS iteration 3: Global Deviance = 6138.415
GAMLSS-RS iteration 4: Global Deviance = 6138.317
GAMLSS-RS iteration 5: Global Deviance = 6138.301
GAMLSS-RS iteration 6: Global Deviance = 6138.296
GAMLSS-RS iteration 7: Global Deviance = 6138.296
```

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