tstab: Threshold stability plots

In longevity: Statistical Methods for the Analysis of Excess Lifetimes

Threshold stability plots

Description

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.

Details

The shape estimates are constrained

Value

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

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")

longevity documentation built on Aug. 22, 2025, 5:11 p.m.