Mean residual life plot — tstab.mrl • mev

Computes mean of sample exceedances over a range of thresholds or for a pre-specified number of largest order statistics, and returns a plot with 95% Wald-based confidence intervals as a function of either the threshold or the number of exceedances. The main purpose is the plotting method, which generates the so-called mean residual life plot. The latter should be approximately linear over the threshold for a generalized Pareto distribution

Usage

tstab.mrl(
  xdat,
  thresh,
  kmin = 10L,
  kmax = length(xdat),
  plot = TRUE,
  level = 0.95,
  xlab = c("thresh", "nexc"),
  type = c("band", "ptwise"),
  ...
)

Arguments

xdat: vector of sample observations
thresh: vector of thresholds
kmin: integer giving the minimum number of exceedances; ignored if thresh is provided. Default to 10
kmax: integer giving the maximum number of exceedances; ignored if thresh is provided. Default to sample size.
plot: logical; if TRUE, call the plot method
level: double giving the level of confidence intervals for the plot, default to 0.95
xlab: string indicating whether to use thresholds (thresh) or number of largest order statistics (nexc) for the x-axis
type: string whether to plot pointwise confidence intervals using segments ("ptwise") or using dashed lines ("band")
...: additional arguments, currently ignored

Value

an invisible list with mean sample exceedances and standard deviation, number of exceedances, threshold

References

Davison, A.C. and R.L. Smith (1990). Models for Exceedances over High Thresholds (with discussion), Journal of the Royal Statistical Society. Series B (Methodological), 52(3), 393–442.

Examples

tstab.mrl(
 xdat = rgp(n = 100, shape = -0.5),
 xlab = "thresh",
 kmax = 50)

tstab.mrl(
 rexp(100),
 thresh = qexp(seq(0, 0.9, by = 0.01)))