## Section 6.1 examples

# Example 1:

observ <- c(0.203, 0.329, 0.382, 0.477, 0.480, 0.503, 0.554, 0.581, 0.621, 0.710)

ks.test(observ, "punif", 0, 1, alternative = "two.sided", exact=T)


# Example 2:

tumor.counts <- c(2,2,4,1,3,1,4,0,2,2,1,1,0,2,2,3,3,3)

mean(tumor.counts)

ks.test(tumor.counts,"ppois",1.75,alternative="less",exact=T)

###### Confidence band for the true c.d.f.:

my.ecdf <- ecdf(observ)

plot(my.ecdf)

# w_0.95 value from Table A13 is 0.409:

myseq <- seq(0,1,by=.001)  # The 'by' value should be small for a nice-looking plot
lines(myseq,pmax(0,my.ecdf(myseq)-.409),col='red')
lines(myseq,pmin(1,my.ecdf(myseq)+.409),col='red')

################################################################

# Section 6.2 examples

#### Lilliefors Test for Normality:

ks.test.stat <- function(x){
mu.hat<-mean(x); sigma.hat <- sd(x);
out <- ks.test(x, "pnorm", mean = mu.hat, sd = sigma.hat)$statistic
return(out)
}

lilliefors.normal.pval <- function(x, nsimul=10000){
mu.hat<-mean(x); sigma.hat <- sd(x); n <- length(x)
T1 <- ks.test.stat((x-mu.hat)/sigma.hat)
mymat<-matrix(rnorm(nsimul*n),nrow=nsimul, ncol=n)
T1distn <- apply(mymat,1,ks.test.stat)
pval <- mean(T1 < T1distn)
out <- list(test.stat=T1, p.value=pval)
return(out)
}

# Trying it on the page 445 data:

my.data.445 <- c(23,23,24,27,29,31,32,33,33,35,36,37,40,42,43,43,44,45,48,48,54,54,56,57,57,58,58,58,58,59,61,61,62,63,64,65,66,68,68,70,73,73,74,75,77,81,87,89,93,97)

lilliefors.normal.pval(my.data.445)

# Trying it on some simulated data sets:

my.data.t <- rt(30,df=4)

my.data.norm <- rnorm(30, mean=30, sd=3)

my.data.exp <- rexp(30, rate=1)

lilliefors.normal.pval(my.data.t)

lilliefors.normal.pval(my.data.norm)

lilliefors.normal.pval(my.data.exp)

#### Lilliefors Test for Exponential Distribution:


lilliefors.expon.ts <- function(x){
z<- x/mean(x)
ecdf.zs<-ecdf(z);
out <- max(c(ecdf.zs(z)-pexp(z), pexp(z)-ecdf.zs(z-.001)))
return(out)
}

wait.times <- faithful$waiting

length(wait.times)

lilliefors.expon.ts(wait.times)

## Shapiro-Wilk Test for Normality:

shapiro.test(my.data.445)

######################################################

# Section 6.3 Examples

## Example 1 (p. 460 data)

x460 <- c(7.6, 8.4, 8.6, 8.7, 9.3, 9.9, 10.1, 10.6, 11.2)

y460 <- c(5.2, 5.7, 5.9, 6.5, 6.8, 8.2, 9.1, 9.8, 10.8, 11.3, 11.5, 12.3, 12.5, 13.4, 14.6)

ks.test(x460, y460, alternative="two.sided", exact=T)

## Example 2

unleaded <- c(21.7, 21.4, 23.3, 22.8)
premium <- c(23.1, 23.5, 22.9, 23.4)

ks.test(unleaded, premium, alternative="greater", exact=T)