# October 2014
# CAMAR

# Introduction to R
# Simple Cookbook Examples

# David L. Homer, FCAS MAAA CERA
# JLT Towers Re

# The goal of this session is to provide simple examples of how to 
# use R with very little knowledge of the entire language. The # examples are contained in this document and can be reproduced by 
# copying from this document and pasting them into an R session.



#### 0. What is R?

# The following description of R is copied from http://www.r-# project.org/

#-----------------------

#	R is a language and environment for statistical computing 
# and graphics. It is a GNU project which is similar to the S 
# language and environment which was developed at Bell Laboratories 
# (formerly AT&T, now Lucent Technologies) by John Chambers and 
# colleagues. R can be considered as a different implementation of 
# S. There are some important differences, but much code written for 
# S runs unaltered under R. 

#	R provides a wide variety of statistical (linear and 
# nonlinear modelling, classical statistical tests, time-series 
# analysis, classification, clustering, ...) and graphical 
# techniques, and is highly extensible. The S language is often the 
# vehicle of choice for research in statistical methodology, and R 
# provides an Open Source route to participation in that activity. 

#	One of R's strengths is the ease with which well-designed 
# publication-quality plots can be produced, including mathematical 
# symbols and formulae where needed. Great care has been taken over 
# the defaults for the minor design choices in graphics, but the 
# user retains full control. 

#	R is available as Free Software under the terms of the 
# Free Software Foundation's GNU General Public License in source 
# code form. It compiles and runs on a wide variety of UNIX 
# platforms and similar systems (including FreeBSD and Linux), 
# Windows and MacOS. 

#----------------------



#### 1. Installation of R


# R installation instructions and software can be obtained at

#	http://www.r-project.org/

	# Select a download site from the Comprehensive R Archive # Network (CRAN)
	# for example, http://lib.stat.cmu.edu/R/CRAN/.
	# Then select "Download R for Windows" and follow the # instructions.

# You can download the software and follow along during the CAMAR # session if you like. It is not necessary.



#### 2. Basics. An R Session. Pasting examples and assigning variables.

# a simple variable assigment can be made with the "<-" symbol # using the c() the concatenate operator

# R is an array based language. Vectors, matrices, and arrays are # natural/common objects in R.

lossratio<-c(.69,.75,.7,.72,.8,.67,.82,.7,.77)


# compute the mean and std
lr.stat<-c(mean(lossratio),sd(lossratio))

# individual items can have names in R
names(lr.stat)<-c("mean","std")



# R allows you to express a sequence with the ":" operator.

year<-2005:2013 # yields the integers 2008,2009,...,2013


# plot loss ratio versus year
plot(year,lossratio,main="Loss Ratio vs Year")

# draw a thick, red, horizontal line representing the mean loss # ratio.
abline(h=mean(lossratio),col="red",lwd=4)


# R sees "\" as a control character so either use "/" or "\\" for # path names.
savePlot("c:/temp/r-camar/plot1.wmf")


### matrices, row and column names,

mm<-matrix(1:9,3,3) ## R loads down the first column then down the # second,..

# unless you ask for loading "byrow"

mm<-matrix(1:9,3,3,byrow=T)

# a matrix can have row and column names

colnames(mm)<-c("A","B","C")
rownames(mm)<-c("R1","R2","R3")



### scan copy from excel

# scan is a convenient way to load a simple list of numbers

# type numbers separated by <enter> into session # followed by an extra <enter> to finish.
aa<-scan()

# scan can also read from the clipboard 
# copy something to the clipboard before running this.
write("1 3.14 528000","clipboard")
bb<-scan("clipboard")



### csv files read write

# write to clipboard, to past to excel
write.table(mm,"clipboard",sep="\t",col.names=NA) 

# read from clipboard, after copying from excel
m2<-read.table("clipboard",sep="\t",header=T,row.names=1) 

# m2 is a data frame, which looks like a matrix but has additional # properties that make it convenient for use with other R functions. # For example, plot(m2).


# write to csv file (easily read by EXCEL)
write.csv(mm,"c:/temp/r-camar/table1.csv") 

# read from the csv file. the row.names=1 is needed to force R to use the row names in column 1.
m2<-read.csv("c:/temp/r-camar/table1.csv",row.names=1) 



#### 3. Simulation

# R does have control structures like loops, but it is generally # better to avoid them if possible
trials<-1000

# draw from a Poisson distribution with lambda=3
sim.n<-rpois(trials,3)

# draw the  claim sizes needed from a Gamma with shape=2 and scale=5000
sim.x<-rgamma(sum(sim.n),shape=2,scale=5000)

# compute the aggregate losses for each trial
sim.cn<-cumsum(c(1,sim.n))
sim.cx<-cumsum(c(0,sim.x))
sim.z<-diff(sim.cx[sim.cn])

mean(sim.z)



#### 4. FFT

# size of discrete transform (powers of 2 help make calculation fast)
buckets<-2^10 


# severity distribution place holder
f<-rep(0,buckets) # rep() function repeats values

# width (entry in f[i] represent the probability of a claim size # of width*(i-1) )
width<-1000

# discretized distribution
# using the functions: pgamma(), diff(), and named parameters of # pgamma(), shape and scale.
f[1:101]<-c(0,diff(pgamma(0:100*width,shape=2,scale=5000)))

# create a function for the probability generating function of the poisson

pgfPoi<-function(f,lambda){
# Poisson PGF
#f-evaluation vector
#lambda-poisson parameter

exp(lambda*(f-1))
}

# compute the aggregate distribution Z=X1 + ... + XN arising from # N claims from a Poisson with lambda=3
# and claim size Xi drawn from a Gamma with shape=2 and scale=5000

z<-Re(fft(pgfPoi(fft(f),3),T)/buckets)

# check mean
check.mean<-c(3*sum(0:(buckets-1)*f)*width,sum(0:(buckets-1)*z)*width)
names(check.mean)<-c("EX*EN","EZ")



# fft versus simulation
plot(ecdf(sim.z))
lines(width*0:99,cumsum(z[1:100]),col="red")