Visualising Claims Frequency

July 28, 2015
By

(This article was first published on Freakonometrics » R-english, and kindly contributed to R-bloggers)

A few years ago, I did publish a post to visualize and empirical claims frequency in a portfolio. I wanted to update the code.

Here is a code to get a dataset,

 sinistre <- read.table("http://freakonometrics.free.fr/sinistreACT2040.txt",header=TRUE,sep=";")
 sinistres=sinistre[sinistre$garantie=="1RC",]
 contrat <- read.table("http://freakonometrics.free.fr/contractACT2040.txt",header=TRUE,sep=";")
 T=table(sinistres$nocontrat)
 T1=as.numeric(names(T))
 T2=as.numeric(T)
 nombre1 = data.frame(nocontrat=T1,nbre=T2)
 I = contrat$nocontrat%in%T1
 T1= contrat$nocontrat[I==FALSE]
 nombre2 = data.frame(nocontrat=T1,nbre=0)
 nombre=rbind(nombre1,nombre2)
 basenb = merge(contrat,nombre)
 head(basenb)
 basesin=merge(sinistres,contrat)
 basesin=basesin[basesin$cout>0,]

and here to get the graphs (thanks Andre for your help to pick the colors, and the style of the graph)

 graph_freq=function(var="ageconducteur",
            levels=c(17,24,34,44,64,110),
            continuous=TRUE,type=1){
   if(continuous==TRUE){X=cut(basenb[,var],levels)}
   if(continuous==FALSE){X=as.factor(basenb[,var])}
   E=basenb$exposition
   Y=basenb$nbre
   FREQ=levels(X)
   moyenne=variance=n=rep(NA,length(FREQ))
   for(k in 1:length(FREQ)){
   moyenne[k] =weighted.mean(Y[X==FREQ[k]]/E[X==FREQ[k]],
   E[X==FREQ[k]])
   variance[k]=weighted.mean((Y[X==FREQ[k]]/E[X==FREQ[k]]-
   moyenne[k])^2,E[X==FREQ[k]])
   n[k]=sum(E[X==FREQ[k]])
    }
  w=barplot(n,names.arg=FREQ,col="yellow",axes=FALSE,
  xlim=c(0,1.2*length(FREQ)+.5),ylim=c(0,2.5*max(n)))
  mid=w[,1]
  axis(4,)
  par(new=TRUE)
  IC1=moyenne+1.96/sqrt(n)*sqrt(variance)
  IC2=moyenne-1.96/sqrt(n)*sqrt(variance)
  moyenneglobale=sum(Y)/sum(E)
 
   if(type==1){
   plot(mid,moyenne,ylim=c(min(c(IC1,IC2)-
        diff(range(c(IC1,IC2)))/4),max(c(IC1,IC2))),type="l",
   col="#FF00FF",axes=FALSE,xlab="",ylab="",
   xlim=c(0,1.2*length(FREQ)+.5))
   for(i in (-10):20) segments(min(mid)-.8,i/40,max(mid)+.8,i/40,lty=2,col="grey")
   segments(mid,IC1,mid,IC2,col="darkorchid4")
   segments(mid-.1,IC1,mid+.1,IC1,col="darkorchid4")
   segments(mid-.1,IC2,mid+.1,IC2,col="darkorchid4")
   points(mid,moyenne,pch=15,col="#FF00FF")
   axis(2,at=seq(0,.3,by=.05))
   abline(h=moyenneglobale,lty=2,col="darkorchid3")}
 
  if(type==2){
    cic=c(100*(IC1/moyenneglobale),100*(IC2/moyenneglobale))
    YL=c(min(cic)-diff(range(cic))/4,max(cic))
   plot(mid,(moyenne/moyenneglobale)*100,ylim=YL,
   type="l",col="#FF00FF",axes=FALSE,xlab="",ylab="",
   xlim=c(0,1.2*length(FREQ)+.5))
   for(i in (-10):20) segments(min(mid)-.8,i*25,max(mid)+.8,i*25,lty=2,col="grey")
   segments(mid,100*(IC1/moyenneglobale),mid,
   (IC2/moyenneglobale)*100,col="darkorchid4")
   segments(mid-.1,100*(IC1/moyenneglobale),mid+.1,
   (IC1/moyenneglobale)*100,col="darkorchid4")
   segments(mid-.1,100*(IC2/moyenneglobale),mid+.1,
   (IC2/moyenneglobale)*100,col="darkorchid4")
   points(mid,100*(moyenne/moyenneglobale),pch=15,col="#FF00FF")
   axis(2,at=seq(0,300,by=50))
 abline(h=100,lty=2,col="darkorchid3")}
 
  mtext("Exposure", 4, line=-2, cex=.8)
  if(type==1){mtext("Annualized Frequency", 
  2, line=+2, cex=.8)}
  if(type==2){mtext("Annualized Frequency (multiplier, %)", 
  2, line=+2, cex=.8)}
   }

For instance, if we consider the age, with the annualized frequency (see on the left axis)

 graph_freq(type=1)

or the multiplier (on a 100 basis)

 graph_freq(type=2)

 

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