Description Usage Arguments Details Value Author(s) References See Also Examples
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).
1 2 3 4 5 6 |
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 |
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/).
A fitted gamlss model
Bob Rigby, Mikis Stasinopoulos and Vlassios Voudouris
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.
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)
|
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)
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