fitTail {gamlss.tr} | 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, trace = 0, ...)
Arguments
y |
The variable of interest |
family |
a |
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 |
type |
which tall needs checking the right (default) of the left |
plot |
whether to plot with default equal |
print |
whether to print the coefficients with default equal |
save |
whether to save the fitted linear model with default equal |
start |
where to start fitting from the tail of the data |
trace |
0: no output 1: minimal 2: print estimates |
... |
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 https://www.gamlss.com/).
Value
A fitted gamlss model
Author(s)
Bob Rigby r.rigby@gre.ac.uk, Mikis Stasinopoulos d.stasinopoulos@gre.ac.uk 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.
Rigby, R. A., Stasinopoulos, D. M., Heller, G. Z., and De Bastiani, F. (2019) Distributions for modeling location, scale, and shape: Using GAMLSS in R, Chapman and Hall/CRC. An older version can be found in https://www.gamlss.com/.
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, https://www.jstatsoft.org/v23/i07/.
Stasinopoulos D. M., Rigby R.A., Heller G., Voudouris V., and De Bastiani F., (2017) Flexible Regression and Smoothing: Using GAMLSS in R, Chapman and Hall/CRC.
(see also https://www.gamlss.com/).
See Also
Examples
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)