# Extreme value modelling Extreme values modelling, including the conditional multivariate approach of Heffernan and Tawn (2004). package ## Details The package was originally called `texmex' for Threshold EXceedances and Multivariate EXtremes. However, it is no longer the case that only threshold excess models are implemented, so the `tex' bit doesn't make sense. So, the package is called `texmex' because it used to be called `texmex'. `evm`: Fit extreme value distributions to data, possibly with covariates. Use maximum likelihood estimation, maximum penalized likelihood estimation, simulate from the posterior distribution or run a parametric bootstrap. Extreme value families include the generalized Pareto distribution (`gpd`) and generalized extreme value (`gev`) distribution. `mex`: Fit multiple, independent generalized Pareto models to the the upper tails of the columns of a data set, and estimate the conditional dependence structure between the columns using the method of Heffernan and Tawn. `bootmex`: Bootstrap estimation for parameters in generalized Pareto models and in the dependence structure. `declust`: Estimation of extremal index and subsequent declustering of dependent sequences using the intervals estimator of Ferro and Segers. ## Examples ```r # Analyse the winter data used by Heffernan and Tawn mymex <- mex(winter, mqu = .7, penalty="none", dqu=.7, which = "NO") plot(mymex) # Only do 10 replicates to keep CRAN checks happy. Do many more in any # real application myboot <- bootmex(mymex, R=10) plot(myboot) mypred <- predict(myboot, pqu=.95) summary(mypred , probs = c( .025, .5, .975 )) # Analyse the liver data included in the package library(MASS) # For the rlm function liver <- liver[liver$ALP.M > 1,] # Get rid of outlier liver$ndose <- as.numeric(liver$dose) alt <- resid(rlm(log(ALT.M) ~ log(ALT.B) + ndose, data=liver, method="MM")) ast <- resid(rlm(log(AST.M) ~ log(AST.B) + ndose, data=liver, method="MM")) alp <- resid(rlm(log(ALP.M) ~ log(ALP.B) + ndose, data=liver, method="MM")) tbl <- resid(rlm(log(TBL.M) ~ log(TBL.B) + ndose, data=liver, method="MM")) r <- data.frame(alt=alt, ast=ast, alp=alp, tbl=tbl) Amex <- mex(r[liver$dose == "A",], mqu=.7) Bmex <- mex(r[liver$dose == "B",], mqu=.7) Cmex <- mex(r[liver$dose == "C",], mqu=.7) Dmex <- mex(r[liver$dose == "D",], mqu=.7) par(mfcol=c(3,3)) plot(Amex) plot(Dmex, col="blue") ## Take a closer look at the marginal behaviour of ALT r$ndose <- liver$ndose altmod1 <- evm(alt, qu=.7, phi = ~ ndose, xi = ~ ndose, data=r) altmod2 <- evm(alt, qu=.7, phi = ~ ndose, data=r) altmod3 <- evm(alt, qu=.7, xi = ~ ndose, data=r) altmod4 <- evm(alt, qu=.7, data=r) # Prefer model 3, with term for xi on basis of AIC balt3 <- evm(alt, qu=.7, xi = ~ ndose, data=r, method="simulate") par(mfrow=c(3,3)) plot(balt3) # use longer burn-in and also thin the output balt3 <- thinAndBurn(balt3,burn=1000,thin=5) plot(balt3) # Get some simulated values for dose D DParam <- predict(balt3,type="lp",newdata=data.frame(ndose=4),all=TRUE)$obj$link[[1]] simD <- rgpd(nrow(DParam), sigma=exp(DParam[,"phi"]), xi=DParam[,"xi"], u=quantile(alt, .7)) # These are simulated residuals. Get some baselines and transform all # to raw scale b <- sample(log(liver$ALT.M), size=nrow(balt3$param), replace=TRUE) res <- exp(b + simD) # estimate quantiles on raw scale quantile(res, prob=c(.5, .75, .9, .95, .99)) # estimate proportion exceeding 3*upper limit of normal mean(res > # 36 * 3) # 36 is the upper limit of normal for ALT ``` ## References J. E. Heffernan and J. A. Tawn, A conditional approach for multivariate extreme values, Journal of the Royal Statistical society B, 66, 497 -- 546, 2004. C.A.T Ferro and J. Segers, Inference for Clusters of Extreme Values, Journal of the Royal Statistical society B, 65, 545 -- 556, 2003. ## Author(s) Harry Southworth, Janet E. Heffernan, Paul D. Metcalfe Maintainer: Harry Southworth URL: https://github.com/harrysouthworth/texmex

texmex-package