---
title: "Comparaison of methods"
output: pdf_document
---

```{r}
PoissonProcess <- function(lambda,T) {
  return(sort(runif(rpois(1,lambda*T),0,T)))

pp1=PoissonProcess(lambda0,Ti)
print(pp1)
plot(c(0,pp1),0:length(pp1),type="s",xlab="time t",ylab="number of events by time t")

pp2=PoissonProcess(lambda1,Ti)
print(pp2)
plot(c(0,pp2),0:length(pp2),type="s",xlab="time t",ylab="number of events by time t")

#time between events 
n1=length(pp1)
tbe1=pp1[2:n1]-pp1[1:n1-1]
tbe1

n2=length(pp2)
tbe2=pp2[2:n2]-pp2[1:n2-1]
tbe2

ks.test(tbe1,pexp,lambda0, alternative="two.sided")

ks.test(tbe2,pexp,lambda1, alternative="two.sided")
```

Local score
```{r}
lambda0 = 1
lambda1 = 2
library("localScore")
E = 10
X = floor(E*log(dexp(tbe1, rate = lambda1)/dexp(tbe1, rate = lambda0)))

max_X = max(X)
min_X = min(X)
P_X = table(factor(X, levels = min_X:max_X))/length(X)

LS=localScoreC(X)$localScore[1]
LS

result = daudin(localScore = LS, score_probabilities = P_X, sequence_length = length(x), sequence_min = min_X, sequence_max = max_X)
result
```