MGL-fitting-mixed • rMGLReg

Case II - modelling Chinese earthquake loss data without covariates

We consider an earthquake loss data set concerning the Chinese mainland, which contains risk information on 291 earthquake events with magnitude greater than 4.0 from 1990 to 2015.
The data set contains:
- year: occurrence year.
- y1: Economic Losses (adjusted). It is expressed in millions of Chinese Yuan (CNY) and are adjusted for inflation to reflect values in 2015.
- yraw: Economic Losses (original).
- death: the number of deaths from an earthquake event.
- inj: the number of injures from an earthquake event.
- magnitude, intensity : the magnitude and maximum intensity of an earthquake event.
- y2: casualties are defined as fatalities and injured people, which are due to damage to occupied buildings.
- u1: cdf of the marginal distribution evaluated at y1.
- u2: cdf of the marginal distribution evaluated at y2.
- u2_: cdf of the marginal distribution evaluated at y2-1.
- f1: pdf of the marginal distribution evaluated at y1.
- f2: pdf of the marginal distribution evaluated at y2.

Load the data

library(rMGLReg)

u <- cbind(earthqCHI$u1, earthqCHI$u2)
u_ <- cbind(earthqCHI$u1, earthqCHI$u2_)
y <- cbind(earthqCHI$y1, earthqCHI$y2)
f <- cbind(earthqCHI$f1, earthqCHI$f2)

obs <- y
U <- u
U_ <- u_
umin <- 20
plot(U)

fitting the mixed copula models

m.norm <- MGL.mle.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f,
                        copula = "Normal", method = "L-BFGS-B",
                        initpar = 0.2)
m.t <- MGL.mle.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f,
                      copula = "t", method = "L-BFGS-B",
                     initpar = c(0.1,3))
m.gumbel <- MGL.mle.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f,
                            copula = "Gumbel",  method = "L-BFGS-B",
                          initpar = c(2))
m.MGLMGA180 <- MGL.mle.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f,
                             copula = "MGL180",  method = "L-BFGS-B",
                             initpar = c(2))
m.MGB2 <- MGL.mle.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f,
                        copula = "MGB2",  method = "L-BFGS-B",
                        initpar = c(1, 4, 0.4))
m.MGLEV180 <- MGL.mle.mixed(obs = y, U = U, U_ = U_, umin = umin, f = f,
                            copula = "MGL-EV180",  method = "L-BFGS-B",
                            initpar = c(0.2))





recap <- function(x){
  res <- c(alpha = x$estimates,
           se = x$se,
           loglike = x$loglike,
           AIC = x$AIC, BIC = x$BIC)
  if(length(res) < 6)
    res <- c(res[1], NA, NA,res[2], NA, NA, res[3:5])
  if (length(res) > 6 & length(res) < 9)
    res <- c(res[1:2], NA, res[3:4], NA, res[5:7])
  res <- as.matrix(res)
  colnames(res) <- x$copula$name
  res}
res.all <- round(cbind(recap(m.norm),
                       recap(m.t),
                       recap(m.gumbel),
                       recap(m.MGLMGA180),
                       recap(m.MGB2),
                       recap(m.MGLEV180)
), 4)
out.com <- t(res.all)
out.com <- out.com[order(out.com[,9], decreasing = T),]
knitr::kable(out.com, digits = 3)
round(out.com, 2)