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Last data update: 2014.03.03

R: For fitting truncated distribution to the tails of data

fitTail

R Documentation

For fitting truncated distribution to the tails of data

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

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

data(film90)
F90 <- film90$borev0
# trucated plots
# 10%
w403<- fitTail(F90, family=WEI3)
plot(w403)
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)