######### DEMO CODE Kapitel 5 ##################
### 19.10.2009 Vorlesung Using R
################################################

## Missing Values ##############################

d.sport <-read.table("http://stat.ethz.ch/Teaching/Datasets/WBL/sport.dat",
                     header=TRUE)

t.kugel <- d.sport[,'kugel']
t.kugel

# create artificial missing data
t.kugel[2] <- NA 

t.kugel

# Which elements of t.kugel are missing?
t.kugel == NA 

is.na(t.kugel)
which(is.na(t.kugel))

# simple statistical functions
mean(t.kugel)

mean(t.kugel,na.rm=TRUE)

#  wilcox.test, t.test use argument "na.action=na.omit"
wilcox.test(t.kugel)
wilcox.test(t.kugel,na.action=na.omit) 

# find out about default na.action:
# getOption("na.action")
# [1] "na.omit"
# weitere Options mit ?na.action

# Drop the NA elements
t.kugel[!is.na(t.kugel)]

# na.omit(df) drops rows of data.frame df
na.omit(t.kugel) #same as above

## ========================================================
## Distributions 
## ========================================================

# The normal distribution is characterized by:
# Density function:
dnorm(0.5)
dnorm(0:5, mean=0, sd=10)

# Cumulative Probability function:
pnorm(c(1, 1.96))

# Quantile function:
qnorm(c(0.25,0.975), mean=0, sd=1)
qnorm(c(0.25,0.975), mean=100, sd=10)

## Visualization of distributions ##############################

# Discrete distributions
plot(0:15, dpois(0:15,lambda=3.5),type="h")
lines(0:15, dpois(0:15,lambda=3.5))

#Continuous distributions
curve(dnorm(x,5,2), xlim=c(-1,10),xlab="x", ylab="density",
      main="normal distribution")

## Random Numbers ##############################
rnorm(5, mean=2, sd=2)

# Poisson distribution: dpois, ppois, qpois, rpois
rpois(10, lambda=3.5)

# uniform distribution
runif(4)

runif(4)

set.seed(27)
runif(1)

set.seed(27)
runif(1)


## ========================================================
## Elements of S: Objects 
## ========================================================

# Get information about the structure of an object:
str(d.sport)

## Object Oriented Programming ##############################
# Each object has a class
class(d.sport)

# spezialised versions of plot etc exist
plot(speer~kugel, data=d.sport)

# The most basic generic function is print! 
# Example:
data(sleep)
r.t <- wilcox.test(extra~group,data=sleep)
print(r.t) # same as simply typing "r.t"
str(r.t) # has all the information,
  ## print.htest selects the test outcome automatically

# ``S4 classes'', package {methods}
methods(print) # to get a list of all print methods available
getAnywhere(print.htest) # to get actual function definition of *methods

# statistical methods attach a specific class attribute to their result
# Example: Linear regression function lm
r.lm <- lm(speer~kugel,data=d.sport)
class(r.lm)

print(r.lm) # actually calls print.lm
summary(r.lm) # actually calls  print.summary.lm

plot(r.lm)  ## explained later (next time?)


## Attributes ##############################

# class, names

names(d.sport)
row.names(d.sport)
dim(d.sport)

# all attributes 
attributes(d.sport)

## Lists ##############################

t.v <- c(Hans=2.0,Fritz=-1.0,Elsa=9.0,Trudi=0.4,Olga=100.0)
t.v

list(t.v, you='nice')
 
## most statistical functions produce a list that collects the results

t.l <- hist(t.kugel, plot=FALSE)
t.l
plot(t.l) # actually calls plot.hist

# Get a sublist of the list
t.l[2:3]
str(t.l[2:3]) # result is also a list

t.l[c("breaks","intensities")]

# Get a component [[ ]]
t.l[[2]]
str(t.l[[2]]) # result is a vector

t.l[['counts']]
t.l$counts

# Note: t.l['counts'] is a list with one component
t.l['counts']
str(t.l['counts'])


d.sport$kugel # returns a vector
d.sport$kugel[4:6]

## Make a list of subsets of a vector:

split(1:7, c(1, 1, 2, 3, 3, 2, 1))

# unlist concatenates all elements of all components into a single vector
unlist(t.l[1:2])

## ========================================================
## ========================================================
## pdf(file="NormalDensityPlot.pdf")
## plot(x=seq(-4,4,by=0.1),
##      y=dnorm(seq(-4,4,by=0.1),mean=0,sd=1),
##      type="l",xaxp=c(-4,4,8),ylim=c(0,0.45),
##      xlab="x",ylab="Density",main="Normal Distribution N(mean=0, sd=1)",
##      asp=10)
## abline(h=0,lty=5)
## abline(v=0.5,lty=3)
## abline(h=dnorm(0.5,mean=0,sd=1),lty=3)
## dev.off()

## pdf(file="NormalCumulativePlot.pdf")
## plot(x=seq(-4,4,by=0.1),
##      y=pnorm(seq(-4,4,by=0.1),mean=0,sd=1),
##      type="l",xaxp=c(-4,4,8),
##      xlab="x",ylab="Cumulative Probability",ylim=c(0,1),
##      main="Normal Distribution N(mean=0, sd=1)", asp=6)
##  abline(h=c(0,1),lty=5,col="grey60")
##  abline(v=1,lty=3)
##  abline(h=pnorm(1,mean=0,sd=1),lty=3)
##  abline(v=1.96,lty=4)
##  abline(h=pnorm(1.96,mean=0,sd=1),lty=4)
##  dev.off()


## pdf(file="NormalQuantilePlot.pdf")
## plot(x=seq(-4,4,by=0.1),
##      y=pnorm(seq(-4,4,by=0.1),mean=0,sd=1),
##      type="l",xaxp=c(-4,4,8),
##      xlab="x",ylab="Cumulative Probability",ylim=c(0,1),
##      main="Normal Distribution N(mean=0, sd=1)",asp=6)
##  abline(h=c(0,1),lty=5,col="grey60")
## abline(h=0.25,lty=3)
## abline(v=qnorm(0.25, mean=0, sd=1),lty=3)
##  abline(h=0.975,lty=4)
##  abline(v=qnorm(0.975, mean=0, sd=1),lty=4)
##  dev.off()