gamlss (version 4.2-8)

loglogSurv: Log-Log Survival function plots for checking the tail behaviour of the data

Description

The log-log Survival functions are design for checking the tails of a single response variable (no explanatory should be involved). There are three different function:

a) the function loglogSurv1() which plot the (left or right) tails of the empirical log-log Survival function against loglog(y), where y is the variable of interest. The coefficient of a linear fit to the plot can be used an estimated for Type I tails.

b) the function loglogSurv2() which plot the (left or right) tails of the empirical log-log Survival function against log(y). The coefficient of a linear fit to the plot can be used an estimated for Type II tails.

c) the function loglogSurv3() which plot the (left or right) tails of the empirical log-log Survival function against y. The coefficient of a linear fit to the plot can be used an an estimated for Type III tails.

The function loglogSurv() combines all the above functions.

The function logSurv() is also design for exploring the tails of a single response variable. It plots the empirical log-survival function against log(y) for specified percentage of the tail and fits a linear, quadratic and exponential curve to the points of the plot. For distributions defined on the positive real line a good linear fit would indicate a Pareto type tail, a good quadratic fit a log-normal type tail and good exponential fit a Weibull type tail. Note that this function is only appropriate to investigate rather heavy tails and it is not very good to discriminate between different type of tails, as the loglogSurv() .

Usage

loglogSurv(y, percentage = 10, howmany = NULL, type = c("right", "left"), 
           plot = TRUE, print = TRUE, save = FALSE)
loglogSurv1(y, percentage = 10, howmany = NULL, type = c("right", "left"), 
           plot = TRUE, print = TRUE, save = FALSE)
loglogSurv2(y, percentage = 10, howmany = NULL, type = c("right", "left"), 
          plot = TRUE, print = TRUE, save = FALSE)
loglogSurv3(y, percentage = 10, howmany = NULL, type = c("right", "left"), 
          plot = TRUE, print = TRUE, save = FALSE)
          
logSurv(y, percentage = 10, howmany = NULL, type = c("right", "left"), 
          plot = TRUE, print = TRUE, save = FALSE)

Arguments

y

a vector, the variable of interest

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

Value

• A plot

Details

The functions loglogSurv1(), loglogSurv3() and loglogSurv3() take the upper (or lower) part of an ordered variable create its empirical survival function and plot the log-log of this functions against log(log(y)), log(y) and y respectively. Then they fit a line to the plot. The coefficients of the line can be interpreted as parameters determined the behaviour of the tail. More details can be found in Chapter 6 of "The Distribution Toolbox of GAMLSS" book which can be found in http://www.gamlss.org/)

References

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
op<-par(mfrow=c(3,1))
loglogSurv1(F90)
loglogSurv2(F90)
loglogSurv3(F90)
par(op)
loglogSurv(F90)

logSurv(F90)