R: Log-Log Survival function plots for checking the tail...

loglogSurv {gamlss} | R Documentation

## 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`

### 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/)

### Value

A plot

### Author(s)

Bob Rigby, Mikis Stasinopoulos and Vlassios Voudouris

### 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. (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.

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 http://www.gamlss.org/).

### Examples

    data(film90)
    F90 <- film90$lborev1
    op<-par(mfrow=c(3,1))
    loglogSurv1(F90)
    loglogSurv2(F90)
    loglogSurv3(F90)
    par(op)
    loglogSurv(F90)

    logSurv(F90)

[Package gamlss version 5.0-2 Index]