第一部门：包evir
一、摸索性函数：

library(evir)
data(danish)
findthresh(danish, 50)

寻找阀值，例子中寻找出来的阀值使得逾越它的为50个数。

data(danish)
emplot(danish) #履历漫衍函数，假如获得的功效是直线那么切合帕累托漫衍。

data(bmw)
exindex(bmw, 100) #预计极值指标

data(danish)
hill(danish) #Hill 图 基于帕累托漫衍

data(danish)
meplot(danish) #简朴均值剩余图
假如图形是向上直线，说明有厚尾，假如直线有正的斜率，说明听从帕累托漫衍。图

形假如是向下的直线，说明薄尾，假如直线0斜率，听从指数漫衍。

data(danish)
records(danish) #极值记录函数
二、漫衍拟合函数
data(bmw)
out <- gev(bmw, “month”) #拟合GEV漫衍。
rlevel.gev(out, 40)

data(nidd.annual)
out <- gumbel(nidd.annual, method = “BFGS”, control = list(maxit = 500)) #

拟合gumbel漫衍。

data(danish)
out <- gpd(danish, 10) #拟合GPD漫衍。

data(danish)
shape(danish) #预计GPD参数图

data(danish)
quant(danish, 0.999) #GPD高分位数尾预计图

data(danish)
out <- gpd(danish, 10) #拟合gpd模子
tp=tailplot(out) #Plot Tail Estimate From GPD Model
gpd.q(tp, 0.999) # Add Quantile Estimates to plot.gpd
gpd.sfall(tp, 0.999) # Add Expected Shortfall Estimates to a GPD Plot

data(danish)
out <- pot(danish, 10)

拟合POT模子

data(bmw)
data(siemens)
out <-gpdbiv(-bmw, -siemens, ne1 = 100, ne2 = 100) #拟合二元gpd模子
interpret.gpdbiv(out, 0.05, 0.05) #表明二元gpd模子
plot(out) #个中有5张图可以画

三、风险损失预计函数
data(danish)
out <- gpd(danish, 10)
riskmeasures(out, c(0.999, 0.9999))

第二部门：包evd
一、摸索型函数
par(mfrow = c(1,2))
smdat1 <- rbvevd(1000, dep = 0.6, model = “log”)
smdat2 <- rbvevd(1000, dep = 1, model = “log”)
chiplot(smdat1) #针对二元极值怀抱依赖度 依赖为1，不然靠近于0.
chiplot(smdat2) # 独立为0

data(portpirie)
tlim <- c(3.6, 4.2)
tcplot(portpirie, tlim) #阀值选择
tcplot(portpirie, tlim, nt = 100, lwd = 3, type = “l”)
tcplot(portpirie, tlim, model = “pp”)

data(portpirie)
clusters(portpirie, 4.2, 3) #甄别超限簇
clusters(portpirie, 4.2, 3, cmax = TRUE) #cmax=F
clusters(portpirie, 4.2, 3, 3.8, plot = TRUE)
clusters(portpirie, 4.2, 3, 3.8, plot = TRUE, lvals = FALSE)
tvu <- c(rep(4.2, 20), rep(4.1, 25), rep(4.2, 20))
clusters(portpirie, tvu, 3, plot = TRUE)

data(portpirie)
exi(portpirie, 4.2, r = 3, ulow = 3.8) #预计极值指标
tvu <- c(rep(4.2, 20), rep(4.1, 25), rep(4.2, 20))
exi(portpirie, tvu, r = 1)
exi(portpirie, tvu, r = 0)

sdat <- mar(100, psi = 0.5)
tlim <- quantile(sdat, probs = c(0.4,0.9))
exiplot(sdat, tlim) #画极值指标图
exiplot(sdat, tlim, r = 4, add = TRUE, lty = 2)
exiplot(sdat, tlim, r = 0, add = TRUE, lty = 4)

data(portpirie)
mrlplot(portpirie) #履历平均剩余寿命图

二、漫衍预计函数
bvdata <- rbvevd(100, dep = 0.7, model = “log”)
abvnonpar(seq(0, 1, length = 10), data=bvdata,convex=T) #二元极值漫衍的依

赖函数的非参数预计
abvnonpar(data = bvdata, method = “pick”, plot = TRUE) #二元极值漫衍的依赖

函数的非参数预计
M1 <- fitted(fbvevd(bvdata, model = “log”))
abvevd(dep = M1[“dep”], model = “log”, plot = TRUE) #二元极值漫衍依赖函数

的参数预计
abvnonpar(data = bvdata, add = TRUE, lty = 2) #二元极值漫衍的依赖函数的非

参数预计

amvevd(dep = 0.5, model = “log”) #多元极值漫衍依赖函数尺度型
s3pts <- matrix(rexp(30), nrow = 10, ncol = 3)
s3pts <- s3pts/rowSums(s3pts)
amvevd(s3pts, dep = 0.5, model = “log”) #多元极值漫衍依赖函数的参数预计
amvevd(dep = 0.05, model = “log”, plot = TRUE, blty = 1)
amvevd(dep = 0.95, model = “log”, plot = TRUE, lower = 0.94)

asy <- list(.4, .1, .6, c(.3,.2), c(.1,.1), c(.4,.1), c(.2,.3,.2))
amvevd(s3pts, dep = 0.15, asy = asy, model = “alog”)
amvevd(dep = 0.15, asy = asy, model = “al”, plot = TRUE, lower = 0.7)

s5pts <- matrix(rexp(50), nrow = 10, ncol = 5)
s5pts <- s5pts/rowSums(s5pts)
sdat <- rmvevd(100, dep = 0.6, model = “log”, d = 5) #生成多元极值漫衍的伪

随机数
amvnonpar(s5pts, sdat, d = 5) #多元极值漫衍依赖函数的非参数预计

amvnonpar(data = sdat, plot = TRUE)
amvnonpar(data = sdat, plot = TRUE, ord = c(2,3,1), lab = LETTERS[1:3])
amvevd(dep = 0.6, model = “log”, plot = TRUE)
amvevd(dep = 0.6, model = “log”, plot = TRUE, blty = 1)

bvdata <- rbvevd(100, dep = 0.7, model = “log”)
qcbvnonpar(c(0.9,0.95), data = bvdata, plot = TRUE)
qcbvnonpar(c(0.9,0.95), data = bvdata, epmar = TRUE, plot = TRUE)

bvdata <- rbvevd(100, dep = 0.7, model = “log”)
M1 <- fitted(fbvevd(bvdata, model = “log”))
hbvevd(dep = M1[“dep”], model = “log”, plot = TRUE)

#p#分页标题#e#

uvdata <- rgev(100, loc = 0.13, scale = 1.1, shape = 0.2) #
trend <-(-49:50)/100
M1 <- fgev(uvdata, nsloc = trend) #极大似然法拟合GEV漫衍
M2 <- fgev(uvdata)
M3 <- fgev(uvdata, shape = 0)
anova(M1, M2, M3) #方差阐明

data(portpirie)
m1 <- fgev(portpirie)
confint(m1) #参数的置信区间
pm1 <- profile(m1) #描写拟合功效，优化功效
plot(pm1) #
confint(pm1) #

uvdata <- rgev(100, loc = 0.13, scale = 1.1, shape = 0.2)
trend <- (-49:50)/100
M1 <- fgev(uvdata, nsloc = trend, control = list(trace = 1))
M2 <- fgev(uvdata)
M3 <- fgev(uvdata, shape = 0)
M4 <- fgev(uvdata, scale = 1, shape = 0)
anova(M1, M2, M3, M4)
par(mfrow = c(2,2))
plot(M2)
M2P <- profile(M2)
plot(M2P)

rnd <- runif(100, min = -.5, max = .5)
fgev(uvdata, nsloc = data.frame(trend = trend, random = rnd))
fgev(uvdata, nsloc = data.frame(trend = trend, random = rnd), locrandom =

0)

uvdata <- rgev(100, loc = 0.13, scale = 1.1, shape = 0.2)
M1 <- fgev(uvdata, prob = 0.1)
M2 <- fgev(uvdata, prob = 0.01)
M1P <- profile(M1, which = “quantile”)
M2P <- profile(M2, which = “quantile”)
plot(M1P)
plot(M2P)

uvdata <- rgev(100,0.13,1.1,0.2)
M1 <- fgev(uvdata)
M1P <- profile(M1)
M1JP <- profile2d(M1, M1P, which = c(“scale”, “shape”))
plot(M1JP)

uvd <- rorder(100, qnorm, mean = 0.56, mlen = 365, j = 2)
forder(uvd, list(mean = 0, sd = 1), distn = “norm”, mlen = 365, j = 2)
forder(uvd, list(rate = 1), distn = “exp”, mlen = 365, j = 2)
forder(uvd, list(scale = 1), shape = 1, distn = “gamma”, mlen = 365, j =

2)
forder(uvd, list(shape = 1, scale = 1), distn = “gamma”, mlen = 365, j =

2)

uvdata <- rgpd(100, loc = 0, scale = 1.1, shape = 0.2)
M1 <- fpot(uvdata, 1)
M2 <- fpot(uvdata, 1, shape = 0)
anova(M1, M2)
par(mfrow = c(2,2))
plot(M1)
M1P <- profile(M1)
plot(M1P)

M1 <- fpot(uvdata, 1, mper = 10)
M2 <- fpot(uvdata, 1, mper = 100)
M1P <- profile(M1, which = “rlevel”, conf=0.975, mesh=0.1)
M2P <- profile(M2, which = “rlevel”, conf=0.975, mesh=0.1)
plot(M1P) #诊断图
plot(M2P)

bvdata <- rbvevd(100, dep = 0.75, model = “log”) #
M1 <- fbvevd(bvdata, model = “log”)
M2 <- fbvevd(bvdata, model = “log”, dep = 0.75)
M3 <- fbvevd(bvdata, model = “log”, dep = 1)
anova(M1, M2)
anova(M1, M3, half = TRUE)

bvdata <- rbvevd(100, dep = 0.6, model = “log”, mar1 = c(1.2,1.4,0.4))
M1 <- fbvevd(bvdata, model = “log”)
M2 <- fbvevd(bvdata, model = “log”, dep = 0.75)
anova(M1, M2)
par(mfrow = c(2,2))
plot(M1) #诊断图
plot(M1, mar = 1)
plot(M1, mar = 2)
par(mfrow = c(1,1))
M1P<-profile(M1, which = “dep”)
plot(M1P)

trend <- (-49:50)/100
rnd <- runif(100, min = -.5, max = .5)
fbvevd(bvdata, model = “log”, nsloc1 = trend)
fbvevd(bvdata, model = “log”, nsloc1 = trend, nsloc2 = data.frame(trend=

trend, random = rnd))
fbvevd(bvdata,model=”log”,nsloc1=trend,nsloc2=data.frame

(trend=trend,random = rnd), loc2random = 0)

bvdata <- rbvevd(100, dep = 1, asy = c(0.5,0.5), model = “anegl”)
anlog <- fbvevd(bvdata, model = “anegl”)
amixed <- fbvevd(bvdata, model = “amix”)
mixed <- fbvevd(bvdata, model = “amix”, beta = 0)
mixed <- fbvevd(bvdata, model = “anegl”, dep = 1, sym = TRUE)
anova(anlog, mixed)
anova(amixed, mixed)

bvdata <- rbvevd(1000, dep = 0.5, model = “log”)
u <- apply(bvdata, 2, quantile, probs = 0.9)
M1 <- fbvpot(bvdata, u, model = “log”)
M2 <- fbvpot(bvdata, u, “log”, dep = 0.5)
anova(M1, M2)

uvdata <- rextreme(100, qnorm, mean = 0.56, mlen = 365)
fextreme(uvdata, list(mean = 0, sd = 1), distn = “norm”, mlen = 365)
fextreme(uvdata, list(rate = 1), distn = “exp”, mlen = 365)
fextreme(uvdata, list(scale = 1), shape = 1, distn = “gamma”, mlen = 365)
fextreme(uvdata, list(shape = 1, scale = 1), distn = “gamma”, mlen = 365)

三、数据模仿函数
library(evd)
marma(100, p = 1, q = 1, psi = 0.75, theta = 0.65) #模仿marmag进程
mar(100, psi = 0.85, n.start = 20) #模仿mar进程
mma(100, q = 2, theta = c(0.75, 0.8)) #模仿mma进程

evmc(100, alpha = 0.1, beta = 0.1, model = “bilog”) #基于极值布局模仿马尔

科夫进程
evmc(100, dep = 10, model = “hr”, margins = “gum”) #

第三部门、包POT
该包主要针对GPD漫衍。这一点初学者应该知道，以免发生不须要的疑问。
大抵可以分为3个进程，即模子摸索阶段、模子拟合阶段、模子诊断阶段。个中摸索

阶段主要包罗摸索数据的大概漫衍形式、数据的阀值选取、数据的超限簇漫衍等。模

型拟合主要包罗GPD模子、二元GPD模子、马尔科夫POT模子。模子诊断主要有绘图诊

断、qq诊断、pp诊断等。尚有一些帮助性功效展示如谱密度、密度等。
模子摸索用到的函数主要有判定相关性函数chimeas()、tsdep.plot()、ts2tsd（）

、tailind.test（） ；超限簇函数clust()；阀值选取函数tcplot()、lmomplot()；

平均剩余寿命函数mrlplot()。阀值选取函数僻静均剩余寿命函数要与超限簇函数配

合利用。
拟合模子的函数主要有fitexi()、fitgpd()、fitbvgpd()、fitmcgpd()、fitpp()。

给出参数置信区间主要有gpd.fishape(）、gpd.fiscale（）、gpd.firl（）[给出的

的是费希尔置信区间]、gpd.pfrl（）、gpd.pfshape（）、gpd.pfshape（）给出

profile置信区间。logLik（）可以给出模子预计的极大似然值。confint（）可以直

接给出置信区间。
模子诊断函数主要有，anova()可以较量差异的模子拟合功效。plot()给出模子诊断

图。convassess()预计参数对初值的敏感性。pp()和qq()检讨拟合功效，假如是直线

#p#分页标题#e#

说明拟合结果精采。retlev()获得return level值。
模子诊断个函数都是以模子拟合功效为操纵工具的。
specdens（）给出拟合功效的谱密度。dens（）,模子的密度图。dexi（）给出机制

指标密度图。diplot（）极值指标扩散图，基于clust()函数的功效。

第一部门：摸索性函数
1.判定相关性函数
library(POT)
mc<-simmc(2000, alpha = 0.9)
mc2<-simmc(1000, alpha = 0.2)

par(mfrow = c(1,2))
chimeas(cbind(mc[1:1000], mc2))

par(mfrow = c(1,2))
chimeas(cbind(mc[seq(1,2000, by = 2)], mc[seq(2,2000,by = 2)]))

par(mfrow = c(1,2))
chimeas(cbind(mc[seq(1,2000, by = 2)], mc[seq(2,2000,by = 2)]), boot

=TRUE)#判定相关性

tsdep.plot(runif(5000), u = 0.95, lag.max = 5)
mc <- simmc(5000, alpha = 0.2)
tsdep.plot(mc, u = 0.95, lag.max = 5) #tsdep.plot判定时间序列的相关性

data(ardieres)
tsd <- ts2tsd(ardieres, 3 / 365) #

plot(ardieres, type = “l”, col = “blue”)
lines(tsd, col = “green”)

A total independence example

x <- rbvgpd(7000, alpha = 1, mar1 = c(0, 1, 0.25))
tailind.test(x)

y <- rbvgpd(7000, alpha = 0.75, model = “nlog”, mar1 = c(0, 1, 0.25),
mar2 = c(2, 0.5, -0.15))
tailind.test(y)

z <- rnorm(7000)
tailind.test(cbind(z, 2*z – 5)) #检讨尾部独立性

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
flows <- ardieres[, “obs”]
lmomplot(flows, identify = FALSE) #L-moment阀值选择，很有用

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
flows <- ardieres[, “obs”]
mrlplot(flows) #履历平均剩余寿命阀值选择，有用

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
flows <- ardieres[, “obs”]
par(mfrow=c(1,2))
tcplot(flows, u.range = c(0, 15) ) #tcplot选择阀值

data(ardieres)
par(mfrow=c(1,2))
clust(ardieres, 4, 10 / 365)
clust(ardieres, 4, 10 / 365, clust.max = TRUE)
clust(ardieres, 4, 10 / 365, clust.max = TRUE, plot = TRUE)

The same but with optional arguments passed to function “plot”

clust(ardieres, 4, 10 / 365, clust.max = TRUE, plot = TRUE,
xlab = “Time (Years)”, ylab = “Flood discharges”,
xlim = c(1972, 1980)) #判定时间序列的超限簇

x<-rgpd(75, 1, 2, 0.1)
pwmu <- fitgpd(x, 1, “pwmu”)
dens(pwmu) #密度图

mc<-simmc(1000, alpha = 0.25)
mc<-qgpd(mc, 0, 1, 0.25)
log <- fitmcgpd(mc, 2, shape = 0.25, scale = 1)
dexi(log, n.sim = 200) #计较极值指标的密度图

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
diplot(ardieres) #极值指标散开图
二、模子拟合
1.拟合极值指标
data(ardieres)
exi<-fitexi(ardieres, 6)
exi
clust(ardieres, 6, tim.cond=exi$tim.cond/365.25,clust.max=TRUE)

2.拟合二元GPD漫衍
x<-rgpd(1000, 0, 1, -0.25)
y<-rgpd(1000, 2, 0.5, 0)
M0<-fitbvgpd(cbind(x,y), c(0, 2))
M1<-fitbvgpd(cbind(x,y), c(0,2), model = “alog”)
anova(M0, M1)

Non regular case

M0 <- fitbvgpd(cbind(x,y), c(0, 2))
M1 <- fitbvgpd(cbind(x,y), c(0, 2), alpha = 1)
anova(M0, M1, half=TRUE)

x <- rgpd(1000, 0, 1, 0.25)
y <- rgpd(1000, 3, 1, -0.25)
ind <- fitbvgpd(cbind(x, y), c(0, 3), “log”)
ind
ind2 <- fitbvgpd(cbind(x, y), c(0, 3), “log”, alpha = 1)
ind2
ind3 <- fitbvgpd(cbind(x, y), c(0, 3), cscale = TRUE)
ind3
dep <- fitbvgpd(cbind(x, x + 3), c(0, 3), “mix”)
dep

x <- rbvgpd(1000, alpha = 0.55, mar1 = c(0,1,0.25), mar2 = c(2,0.5,0.1))
Mlog <- fitbvgpd(x, c(0, 2), “log”)
layout(matrix(c(1,1,2,2,0,3,3,0), 2, byrow = TRUE))
plot(Mlog)

3．拟合GPD漫衍

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
fitted <- fitgpd(ardieres[, “obs”], 6, ‘mle’)
npy <- fitted$nat / 33.4 ##33.4 is the total record length (in year)
par(mfrow=c(2,2))
plot(fitted, npy = npy)

x<-rgpd(1000, 0, 1, -0.15)
M0<-fitgpd(x, 0, shape = -0.15)
M1<-fitgpd(x, 0)
anova(M0, M1)

x <- rgpd(100, 0, 1, 0.25)
mle <- fitgpd(x, 0)
confint(mle, prob = 0.2)
confint(mle, parm = “shape”) #预计GPD参数置信区间

data(ardieres)
ardieres <- clust(ardieres, 4, 10 / 365, clust.max = TRUE)
fitted <- fitgpd(ardieres[,”obs”], 5, ‘mle’)
gpd.fishape(fitted)
gpd.fiscale(fitted) #费希尔置信区

#p#分页标题#e#

data(ardieres)
events <- clust(ardieres, u = 4, tim.cond = 8 / 365,
clust.max = TRUE)
MLE <- fitgpd(events[, “obs”], 4, ‘mle’)
gpd.pfshape(MLE, c(0, 0.8)) #profile 置信区间
rp2prob(10, 2)
gpd.pfrl(MLE, 0.95, c(12, 25))

Univariate Case

x <- rgpd(30, 0, 1, 0.2)
med <-fitgpd(x, 0, “med”)
convassess(med)

Bivariate Case

x <- rbvgpd(50, model = “log”, alpha = 0.5, mar1 = c(0, 1, 0.2))
log <- fitbvgpd(x, c(0,0))
convassess(log) #参数的不变性

x <- rgpd(500, 0, 1, -0.15)
mle <- fitgpd(x, 0)
logLik(mle) #GPD的极大似然值
convassess（mle）
4.拟合马尔科夫POT模子
mc <- simmc(200, alpha = 0.5)
mc <- qgpd(mc, 0, 1, 0.25)
Mclog <- fitmcgpd(mc, 1)
par(mfrow=c(2,2))
rlMclog <- plot(Mclog)
rlMclog(T = 3)

data(ardieres)
Mcalog <- fitmcgpd(ardieres[,”obs”], 5, “alog”)
retlev(Mcalog, opy = 990)

x <- rgpd(200, 1, 2, 0.25)
mle <- fitgpd(x, 1, “mle”)$param
pwmu <- fitgpd(x, 1, “pwmu”)$param
pwmb <- fitgpd(x, 1, “pwmb”)$param
pickands <- fitgpd(x, 1, “pickands”)$param ##Check if Pickands estimates

are valid or not !!!

med <- fitgpd(x, 1, “med”, ##Sometimes the fitting algo is not
start = list(scale = 2, shape = 0.25))$param ##accurate. So specify

good starting values is

a good idea.

mdpd <- fitgpd(x, 1, “mdpd”)$param
lme <- fitgpd(x, 1, “lme”)$param
mple <- fitgpd(x, 1, “mple”)$param
ad2r <- fitgpd(x, 1, “mgf”, stat = “AD2R”)$param

print(rbind(mle, pwmu, pwmb, pickands, med, mdpd, lme,mple, ad2r))

Use PWM hybrid estimators

fitgpd(x, 1, “pwmu”, hybrid = FALSE)

Now fix one of the GPD parameters

Only the MLE, MPLE and MGF estimators are allowed !

fitgpd(x, 1, “mle”, scale = 2)
fitgpd(x, 1, “mple”, shape = 0.25)

mc <- simmc(1000, alpha = 0.25)
mc <- qgpd(mc, 0, 1, 0.25)

A first application when marginal parameter are estimated

fitmcgpd(mc, 0)

Another one where marginal parameters are fixed

mle <- fitgpd(mc, 0)
fitmcgpd(mc, 0, scale = mle$param[“scale”], shape = mle$param[“shape”])

x<-rgpd(1000, 0, 1, 0.2)
fitpp(x, 0) #拟合PP要领

x <- rbvgpd(1000, alpha = 0.9, model = “mix”, mar1 = c(0,1,0.25),
mar2 = c(2,0.5,0.1))
Mmix <- fitbvgpd(x, c(0,2), “mix”)
pickdep(Mmix) #pickand 相关性检讨

x <- rgpd(75, 1, 2, 0.1)
pwmb <- fitgpd(x, 1, “pwmb”)
pp(pwmb)

ppplot，检讨模子，假如是直线，模子拟合很好。

x <- rgpd(75, 1, 2, 0.1)
pwmu <- fitgpd(x, 1, “pwmu”)
qq(pwmu)#检讨模子，直线。

x <- rbvgpd(1000, alpha = 0.25, mar1 = c(0, 1, 0.25))
Mlog <- fitbvgpd(x, c(0, 0), “log”)
retlev(Mlog)

x <- rgpd(75, 1, 2, 0.1)
pwmu <- fitgpd(x, 1, “pwmu”)
rl.fun <- retlev(pwmu)
rl.fun(100)

par(mfrow=c(1,2))

Spectral density for a Markov Model

mc <- simmc(1000, alpha = 0.25, model = “log”)
mc <- qgpd(mc, 0, 1, 0.1)
Mclog <- fitmcgpd(mc, 0, “log”)
specdens(Mclog)

Spectral density for a bivariate POT model

x <- rgpd(500, 5, 1, -0.1)
y <- rgpd(500, 2, 0.2, -0.25)
Manlog <- fitbvgpd(cbind(x,y), c(5,2), “anlog”)
specdens(Manlog) #谱密度

第四部门：包fExtremes
包中寻找阀值的函数为findThreshold（），blockMaxima（），pointProcess

(),deCluster()。机制指标预计函数、exindexPlot()、exindexesPlot()，留意这两

者的差异。emdPlot（）履历漫衍函数。qqparetoPlot（）、mePlot（）、mrlPlot（

）、msratioPlot（）、recordsPlot（）、ssrecordsPlot（）、sllnPlot（）、

lilPlot（）、xacfPlot（）、ghMeanExcessFit（）、hypMeanExcessFit（）、

nigMeanExcessFit（）、ghtMeanExcessFit（）
blockTheta()、clusterTheta()、runTheta()、ferrosegersTheta()计较Theta。

计较VaR和ES的函数别离是VaR()和CVaR()。
包内里有两个模子演示函数别离是tailSlider()、gevSlider()、gpdSlider()。
library(fExtremes)。
模仿GEV漫衍gevSim（）。gumbelSim（）。gpdSim()。thetaSim()。
拟合模子的函数有gevFit()、gumbelFit（）、gpdFit()看拟合功效用summay()，诊

断模子plot()。tailPlot()、tailRisk()、gpdTailPlot（）、gpdShapePlot（）。
gevMoments（）模仿gev进程并返回真是均值等。gpdMoments（）。
hillplot()、shaparmPlot()，shaparmPickands(),shaparmHill()，shaparmDEHaan

（）。gpdQPlot()、gpdQuantPlot（）、
计较风险损失的函数tailRisk()、gpdRiskMeasures（）、gpdSfallPlot（）、VaR()

、CVaR()
gevrlevelPlot()
x = as.timeSeries(data(danishClaims))
findThreshold(x, n = c(10, 50, 100)) #寻找阀值

BMW = as.timeSeries(data(bmwRet))
colnames(BMW) = “BMW.RET”
head(BMW)
x=blockMaxima( BMW, block = 65)
head(x)
y=blockMaxima(-BMW, block = 65) #寻找超限数据集
head(y)
y = blockMaxima(-BMW, block = “monthly”)
head(y)

PP=pointProcess(x = -BMW, u = quantile(as.vector(x), 0.75))
PP
nrow(PP)

DC=deCluster(x = PP, run = 15, doplot = TRUE)
DC
nrow(DC)

Extremal Index for the right and left tails

of the BMW log returns:

#p#分页标题#e#

data(bmwRet)
par(mfrow = c(2, 2), cex = 0.7)
exindexPlot( as.timeSeries(bmwRet), block = “quarterly”)
exindexPlot(-as.timeSeries(bmwRet), block = “quarterly”)

Extremal Index for the right and left tails

of the BMW log returns:

exindexesPlot( as.timeSeries(bmwRet), block = 65)
exindexesPlot(-as.timeSeries(bmwRet), block = 65)

留意两者的差异，返回的参数是差异的。

gevSlider(method = “dist”)
gevSlider(method = “rvs”)

这个很好玩儿。对付gpd同样合用。

摸索性数据阐明函数：

Simulate GEV Data, use default length n=1000

x = gevSim(model = list(xi = 0.25, mu = 0 , beta = 1), n = 1000)
head(x)

gumbelSim –

Simulate GEV Data, use default length n=1000

x = gumbelSim(model = list(xi = 0.25, mu = 0 , beta = 1))

gevFit –

Fit GEV Data by Probability Weighted Moments:

fit = gevFit(x, type = “pwm”)
print(fit)

summary –

Summarize Results:

par(mfcol = c(2, 2))
summary(fit)

gpdSim –

x = gpdSim(model = list(xi = 0.25, mu = 0, beta = 1), n = 1000)

gpdFit –

par(mfrow = c(2, 2), cex = 0.7)
fit = gpdFit(x, u = min(x), type = “pwm”)
print(fit)
summary(fit)

gevMoments:

Returns true mean and variance:

gevMoments(xi = 0, mu = 0, beta = 1)

gevSim –

Simulate GEV Data, use default length n=1000

x = gevSim(model = list(xi = 0.25, mu = 0 , beta = 1), n = 1000)
head(x)

gumbelSim –

Simulate GEV Data, use default length n=1000

x = gumbelSim(model = list(xi = 0.25, mu = 0 , beta = 1))

gevFit –

Fit GEV Data by Probability Weighted Moments:

fit = gevFit(x, type = “pwm”)
print(fit)

summary –

Summarize Results:

par(mfcol = c(2, 2))
summary(fit)

Load Data:

BMW Stock Data – negative returns

x = -as.timeSeries(data(bmwRet))
colnames(x)<-“BMW”
head(x)

gevFit –

Fit GEV to monthly Block Maxima:

fit = gevFit(x, block = “month”)
print(fit)

gevrlevelPlot –

Return Level Plot:

gevrlevelPlot(fit)

预计排雷托漫衍

gpdSim –

x = gpdSim(model = list(xi = 0.25, mu = 0, beta = 1), n = 1000)

gpdFit –

par(mfrow = c(2, 2), cex = 0.7)
fit = gpdFit(x, u = min(x), type = “pwm”)
print(fit)
summary(fit)

Load Data:

danish = as.timeSeries(data(danishClaims))

Tail Plot:

x = as.timeSeries(data(danishClaims))
fit = gpdFit(x, u = 10)
tailPlot(fit)

Try Tail Slider:

tailSlider(x)

Tail Risk:

tailRisk(fit)

GPD有关函数

gpdQPlot estimation of high quantiles,
gpdQuantPlot variation of high quantiles with threshold,
gpdRiskMeasures prescribed quantiles and expected shortfalls,
gpdSfallPlot expected shortfall with confidence intervals,
gpdShapePlot variation of shape with threshold,
gpdTailPlot plot of the tail,
tailPlot ,
tailSlider ,
tailRisk .
gpdSim generates data from the GPD,
gpdFit fits empirical or simulated data to the distribution,
print print method for a fitted GPD object of class …,
plot plot method for a fitted GPD object,
summary summary method for a fitted GPD object.

gevSim generates data from the GEV distribution,
gumbelSim generates data from the Gumbel distribution,
gevFit fits data to the GEV distribution,
gumbelFit fits data to the Gumbel distribution,
print print method for a fitted GEV object,
plot plot method for a fitted GEV object,
summary summary method for a fitted GEV object,
gevrlevelPlot k-block return level with confidence intervals.

可以直接计较VaR CVaR
?VaR
?CVaR

Search Results
The search string was “garch”

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bayesGARCH
Bayesian Estimation of the GARCH(1,1) Model with Student-t Innovations
Garch
Daily Observations on Exchange Rates of the US Dollar Against Other

Currencies
fGarch-package
GARCH Modelling Package
absMoments
Absolute Moments of GARCH Distributions
fGARCH-class
Class “fGARCH”
fGARCHSPEC-class
Class “fGARCHSPEC”
garchFit
Univariate GARCH Time Series Fitting
garchFitControl
GARCH Fitting Algorithms and Control
garchSim
Univariate GARCH/APARCH Time Series Simulation
garchSpec
Univariate GARCH Time Series Specification
coef-methods
GARCH Coefficients Methods
fitted-methods
Extract GARCH Model Fitted Values
formula-methods
Extract GARCH Model formula
plot-methods
GARCH Plot Methods
predict-methods
GARCH Prediction Function
residuals-methods
Extract GARCH Model Residuals
show-methods
GARCH Modelling Show Methods
summary-methods
GARCH Summary Methods
volatility-methods
Extract GARCH Model Volatility
RcmdrepackPlugin-internal
Internal RcmdrepackPlugin objects
gBox
Generalized Portmanteau Tests for GARCH Models
garch.sim
Simulate a GARCH process
garch-methods
Methods for Fitted GARCH Models
garch
Fit GARCH Models to Time Series
summary.garch
Summarizing GARCH Model Fits