Nothing
epstein<-function (x, alternative = "two.sided",exact=FALSE)
{
# 11.1. A Test of Exponentiality versus IFR Alternatives (Epstein)
# Assumptions:
# A1. x_{i} ~ iid F (F is continuous)
# A2. F(a) = 0 for a<0.
# If exact == FALSE, then the large sample approximation will be used if n>=9
p.sum.unif= function (x,n)
{
# Finds the probability of the sum of n uniform(0,1) r.v.'s
# Formula from An Introduction to Probability Theory and It's Applications by William Feller volume 1 ed. 3 (pg 285)
# (1/n!)Sum_{i=0}^{n}[(-1^i)(nCi)(x-i)^n] with 0<=i<x
s = 0
for(i in 0:n){
s = s + ((-1)^i)*choose(n,i)*max(0,(x-i))^n
}
return(s/factorial(n))
}
# The next three lines are modified from fisher.test to get the correct alternative
# hypotheses. Citation needed?
alternative <- char.expand(alternative, c("two.sided", "dfr", "ifr"))
if (length(alternative) > 1L || is.na(alternative))
stop("alternative must be \"two.sided\", \"dfr\" or \"ifr\"")
x.ord = sort(x) #ordered values
n = length(x)
D = n*x.ord[1] # D_{1}
for(i in 2:n){
D = c(D, (n-i+1)*(x.ord[i]-x.ord[i-1]))
}
S = cumsum(D)
E = sum(S[1:(n-1)])/S[n] #E is script E in the text
# large sample approximation
if(n>=9){
if(exact==FALSE){
E.star = (E-((n-1)/2))/sqrt((n-1)/12)
if(alternative=="dfr"){
p=pnorm(E.star)
} else if(alternative=="ifr"){
p=pnorm(E.star, lower.tail=F)
} else if(alternative=="two.sided"){
p=2*pnorm(abs(E.star), lower.tail=FALSE)
}
cat("E*=", E.star, "\n", "p=", p,"\n")
return(list(E=E.star,prob=p))
}
}
# Exact Test
if(alternative=="dfr"){
p=1-p.sum.unif(n-1-E,n-1)
}else if(alternative=="ifr"){
p=1-p.sum.unif(E,n-1)
} else if(alternative=="two.sided"){
p=2*min(1-p.sum.unif(n-1-E,n-1),1-p.sum.unif(E,n-1))
}
cat("E=", E, "\n", "p=", p,"\n")
return(list(E=E,p=p))
}
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