Figurer til noterne i Grundlæggende livsforsikringsmatematik (Liv1)

figurer

require(ggplot2)
require(eha)
library(ggplot2)
library(eha)

alpha = 5.0 * (10.0 ** -4.0)
beta = 7.5858 * (10.0 ** -5.0)
gamma = log (1.09144)

GompertzMakeham <- function(xvar) { 
  alpha + beta * exp(gamma * xvar) 
}

GompertzMakeham70 <- function(x) ifelse(x >= 70, GompertzMakeham(x), NA) 

xAxisBreaks = c(0,10,20,30,40,50,60,70,80,90,100)
yAxisBreaks = xAxisBreaks / 100

ggplot(data.frame(t=c(0, 100)), aes(x=t)) + 
  stat_function(fun = pmakeham, arg=list(shape = c(beta, alpha), scale=1.0/gamma, lower.tail = FALSE), geom="line") + 
  stat_function(fun = pmakeham, arg=list(shape = c(beta, alpha), scale=1.0/gamma, lower.tail = TRUE), geom="line", linetype=2) +
  ggtitle(expression(paste("Figure 3.1: The G82M mortality law: F broken line, ", bar(F) ," whole line"))) +
  scale_x_continuous(breaks=xAxisBreaks) +
  scale_y_continuous(breaks=yAxisBreaks) +
  theme(axis.title.y=element_blank(), text = element_text(size = 8))
ggsave("figure3.1.png", width=15, height=8, units="cm")

ggplot(data.frame(t=c(0, 100)), aes(x=t)) + 
  stat_function(fun = dmakeham, arg=list(shape = c(beta, alpha), scale=1.0/gamma), geom="line") + 
  ggtitle(expression(paste("Figure 3.2: The density ", f, " for the G82M mortality law."))) + 
  scale_x_continuous(breaks=xAxisBreaks) +
  theme(axis.title.y=element_blank(), text = element_text(size = 8))
ggsave("figure3.2.png", width=15, height=8, units="cm")

ggplot(data.frame(t=c(0, 100)), aes(x=t)) + 
  stat_function(fun = hmakeham, arg=list(shape = c(beta, alpha), scale=1.0/gamma), geom="line") + 
  ggtitle(expression(paste("Figure 3.3: The force of mortality ", mu, " for the G82M mortality law"))) + 
  scale_x_continuous(breaks=xAxisBreaks) +
  theme(axis.title.y=element_blank(), text = element_text(size = 8))
ggsave("figure3.3.png", width=15, height=8, units="cm")

ggplot(data.frame(x = c(0, 100)), aes(x)) +
  stat_function(fun = GompertzMakeham70) +  
  ggtitle(expression(paste("Figure 3.6: The force of mortality", mu, "(t|70) = ", mu,"(70 + t), t > 0, for the G82M mortality law."))) + 
  scale_x_continuous(breaks=xAxisBreaks) +
  theme(axis.title.y=element_blank(), text = element_text(size = 8)) 
ggsave("figure3.6.png", width=15, height=8, units="cm")

(xmax <- qexp(0.995, rate=0.2))
xvals <- seq(0, xmax, length=100)
qplot(xvals, pexp(xvals, rate=0.2), geom="line")  +
  stat_function(fun=pexp, geom="line", colour="blue", arg=list(rate=2)) + 
  stat_function(fun=dexp, geom="line",  arg=list(rate=0.2)) +  
  stat_function(fun=dexp, geom="line", colour="blue", arg=list(rate=2)) +
  ggtitle(expression(paste("Figure 3.7: Two exponential laws with intensities ", lambda[1], " and ",
                           lambda[2], " such that ", lambda[1] < lambda[2], "; ", bar(F)[1], " and ", bar(F)[2], " blue line, ",
                           f[1], " and ", f[2], " black line"))) +
  theme(axis.title.x=element_blank(), axis.title.y=element_blank(), text = element_text(size = 8)) 
ggsave("figure3.7.png", width=15, height=8, units="cm")