Threshold stability plots

The generalized Pareto and exponential distribution are threshold stable. This property, which is used for extrapolation purposes, can also be used to diagnose goodness-of-fit: we expect the parameters \(\xi\) and \(\tilde{\sigma} = \sigma + \xi u\) to be constant over a range of thresholds. The threshold stability plot consists in plotting maximum likelihood estimates with pointwise confidence interval. This function handles interval truncation and right-censoring.

Usage

tstab(
  time,
  time2 = NULL,
  event = NULL,
  thresh = 0,
  ltrunc = NULL,
  rtrunc = NULL,
  type = c("right", "left", "interval", "interval2"),
  family = c("gp", "exp"),
  method = c("wald", "profile"),
  level = 0.95,
  plot = TRUE,
  plot.type = c("base", "ggplot"),
  which.plot = c("scale", "shape"),
  weights = NULL,
  arguments = NULL,
  ...
)

Arguments

time

excess time of the event of follow-up time, depending on the value of event

time2

ending excess time of the interval for interval censored data only.

event

status indicator, normally 0=alive, 1=dead. Other choices are TRUE/FALSE (TRUE for death). For interval censored data, the status indicator is 0=right censored, 1=event at time, 2=left censored, 3=interval censored. Although unusual, the event indicator can be omitted, in which case all subjects are assumed to have experienced an event.

thresh

vector of thresholds

ltrunc

lower truncation limit, default to NULL

rtrunc

upper truncation limit, default to NULL

type

character string specifying the type of censoring. Possible values are "right", "left", "interval", "interval2".

family

string; distribution, either generalized Pareto (gp) or exponential (exp)

method

string; the type of pointwise confidence interval, either Wald (wald) or profile likelihood (profile)

level

probability level for the pointwise confidence intervals

plot

logical; should a plot be returned alongside with the estimates? Default to TRUE

plot.type

string; either base for base R plots or ggplot for ggplot2 plots

which.plot

string; which parameters to plot;

weights

weights for observations

arguments

a named list specifying default arguments of the function that are common to all elife calls

...

additional arguments for optimization, currently ignored.

Value

an invisible list with pointwise estimates and confidence intervals for the scale and shape parameters

Details

The shape estimates are constrained

See also

tstab.gpd from package mev, gpd.fitrange from package ismev or tcplot from package evd, among others.

Examples

set.seed(1234)
n <- 100L
x <- samp_elife(n = n,
                scale = 2,
                shape = -0.2,
                lower = low <- runif(n),
                upper = upp <- runif(n, min = 3, max = 20),
                type2 = "ltrt",
                family = "gp")
tstab_plot <- tstab(time = x,
                    ltrunc = low,
                   rtrunc = upp,
                   thresh = quantile(x, seq(0, 0.5, length.out = 4)))


plot(tstab_plot, plot.type = "ggplot")