# fitTail: For fitting truncated distribution to the tails of data In gamlss.tr: Generating and Fitting Truncated `gamlss.family' Distributions

## Description

There are two functions here. The function fitTail() which fits a truncated distribution to certain percentage of the tail of a response variable and the function fitTailAll() which does a sequence of truncated fits. Plotting the results from those fits is analogous to the Hill plot, Hill (1975).

## Usage

 1 2 3 4 5 fitTail(y, family = "WEI3", percentage = 10, howmany = NULL, type = c("right", "left"), ...) fitTailAll(y, family = "WEI3", percentage = 10, howmany = NULL, type = c("right", "left"), plot = TRUE, print = TRUE, save = FALSE, start = 5)

## Arguments

 y The variable of interest family a gamlsss.family distribution percentage what percentage of the tail need to be modelled, default is 10% howmany how many observations in the tail needed. This is an alternative to percentage. If it specified it take over from the percentage argument otherwise percentage is used. type which tall needs checking the right (default) of the left plot whether to plot with default equal TRUE print whether to print the coefficients with default equal TRUE save whether to save the fitted linear model with default equal FALSE start where to start fitting from the tail of the data ... for further argument to the fitting function

## Details

The idea here is to fit a truncated distribution to the tail of the data. Truncated log-normal and Weibull distributions could be appropriate distributions. More details can be found in Chapter 6 of "The Distribution Toolbox of GAMLSS" book which can be found in http://www.gamlss.org/).

## Value

A fitted gamlss model

## Author(s)

Bob Rigby, Mikis Stasinopoulos and Vlassios Voudouris

## References

Hill B. M. (1975) A Simple General Approach to Inference About the Tail of a Distribution Ann. Statist. Volume 3, Number 5, pp 1163-1174.

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. (2006) Instructions on how to use the GAMLSS package in R. Accompanying documentation in the current GAMLSS help files, (see also http://www.gamlss.org/).

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, http://www.jstatsoft.org/v23/i07.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 data(film90) F90 <- exp(film90\$lborev1)# original scale # trucated plots # 10% w403<- fitTail(F90, family=WEI3) qqnorm(resid(w403)) abline(0,1, col="red") ## Not run: # hill -sequential plot 10 w1<-fitTailAll(F90) # plot sigma plot(w1[,2]) #----------------- #LOGNO l403<- fitTail(F90, family=LOGNO) plot(l403) qqnorm(resid(l403)) abline(0,1) # hill -sequential plot 10 l1<-fitTailAll(F90, family=LOGNO) plot(l1[,2]) #------------------------- ## End(Not run)

### Example output

Loading required package: gamlss.dist
Loading required package: MASS
Loading required package: gamlss
Loading required package: splines
Loading required package: gamlss.data

Attaching package: 'gamlss.data'

The following object is masked from 'package:datasets':

sleep

Loading required package: nlme
Loading required package: parallel
**********   GAMLSS Version 5.1-3  **********
For more on GAMLSS look at http://www.gamlss.org/
Type gamlssNews() to see new features/changes/bug fixes.

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******************************************************************
Summary of the Quantile Residuals
mean   =  -0.007390017
variance   =  1.026731
coef. of skewness  =  -0.03727448
coef. of kurtosis  =  2.74619
Filliben correlation coefficient  =  0.9989058
******************************************************************
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1: In MLE(ll2, start = list(eta.mu = eta.mu, eta.sigma = eta.sigma),  :
possible convergence problem: optim gave code=1 false convergence (8)
2: In MLE(ll2, start = list(eta.mu = eta.mu, eta.sigma = eta.sigma),  :
possible convergence problem: optim gave code=1 false convergence (8)
3: In MLE(ll2, start = list(eta.mu = eta.mu, eta.sigma = eta.sigma),  :
possible convergence problem: optim gave code=1 false convergence (8)
4: In MLE(ll2, start = list(eta.mu = eta.mu, eta.sigma = eta.sigma),  :
possible convergence problem: optim gave code=1 false convergence (8)
5: In MLE(ll2, start = list(eta.mu = eta.mu, eta.sigma = eta.sigma),  :
possible convergence problem: optim gave code=1 false convergence (8)
6: In MLE(ll2, start = list(eta.mu = eta.mu, eta.sigma = eta.sigma),  :
possible convergence problem: optim gave code=1 false convergence (8)
7: In MLE(ll2, start = list(eta.mu = eta.mu, eta.sigma = eta.sigma),  :
possible convergence problem: optim gave code=1 false convergence (8)

gamlss.tr documentation built on May 2, 2019, 7:15 a.m.