mobirep (version 0.2.3)

Cond.mod.ap: Fits the bivariate conditional extremes model

Description

Fits the bivariate conditional extremes model (from Heffernan and Tawn (2004) and texmex R package) and provides estimates of a conditional or joint exceedance level curve with a probability corresponding to 'pobj'. Also provides estimates of dependence measures.

Usage

Cond.mod.ap(
  u2,
  tr1,
  tr2,
  tsim,
  num.sim,
  pobj,
  interh = "comb",
  mar1,
  mar2,
  px,
  py
)

Arguments

u2

Two column data frame

tr1

extreme threshold for first variable

tr2

extreme threshold for second variable

tsim

Prediction quantile. The quantile of the conditioning variable above which it will be simulated for importance sampling based prediction (from texmex)

num.sim

The number of simulated observations to be generated for prediction (from texmex)

pobj

objective joint return period modelled with the conditional extremes model

interh

type of hazard interrelation 'comb' for compound (joint exceedance probability) and 'casc' for cascade (conditional porbability)

mar1

Values of the first margin

mar2

Values of the second margin

px

Uniform values of the first margin with a mixed distribution (empirical below and gpd above a threshold)

py

Uniform values of the second margin with a mixed distribution (empirical below and gpd above a threshold)

Value

a list containing the following:

• jline - data frame of the objective level curve with the selected return period 'pobj'

• onlysim - data frame of simulated extreme data for the two variables

• etaHT - threshold dependent extremal dependence measure

• chiHT - threshold dependent coefficient of tail dependence

References

Tilloy, A., Malamud, B.D., Winter, H. and Joly-Laugel, A., 2020. Evaluating the efficacy of bivariate extreme modelling approaches for multi-hazard scenarios. Natural Hazards and Earth System Sciences, 20(8), pp.2091-2117.

Heffernan, J.E. and Tawn, J.A., 2004. A conditional approach for multivariate extreme values (with discussion). Journal of the Royal Statistical Society: Series B (Statistical Methodology), 66(3), pp.497-546.

See Also

mex

Examples

# NOT RUN {
# Import data
data(porto)
tr1=0.9
tr2=0.9
fire01meantemp=na.omit(fire01meantemp)
u=fire01meantemp

#Compute uniform margins
marg=Margins.mod(tr1,tr2,u=fire01meantemp)
kk=marg$uvar
pp=marg$uvar_ext
uu=marg$val_ext

upobj=0.001
t.sim=0.98
interh="comb"
 
# }
# NOT RUN {
# Fit conditional extremes model
condexres<-Cond.mod.ap(u2=u,tr1,tr2,tsim=t.sim,num.sim=10000,
pobj=upobj,mar1=uu[,1],mar2=uu[,2],px=pp[,1],py=pp[,2],interh=interh)

 plot(condexres$jline)
 
# }