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Scan-Statistics-Project-4Y-INSA
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Merge branch 'main' of https://github.com/Paul-Corbalan/Scan-Statistics-Project-4Y-INSA

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Paul-Corbalan 2022-03-08 10:43:00 +01:00
parent c9c76fcc1d 966dccd95e
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69
Dataset_study.rmd
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@ -133,16 +133,9 @@ Hence, we can see that, in the dataset `x`, wihtout any irregularities, there ar
Now we will use another method using the uniform distribution in order to implement a Poisson Process.
```{r}
PoissonProcess <- function(lambda,T) {
return(sort(runif(rpois(1,lambda*T),0,T)))
}
lambda0=2
lambda1=3
Ti=10
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")
@ -164,9 +157,6 @@ ks.test(tbe1,pexp,lambda0, alternative="two.sided")
ks.test(tbe2,pexp,lambda1, alternative="two.sided")
```
The Kolmogorov-Smirnov test rejects the hypothesis that the time between events sequence is following an exponential distribution.
@ -176,54 +166,73 @@ Je reprends votre code pour faire un data set :
```{r}
PoissonProcess <- function(lambda,T) {
return(sort(runif(rpois(1,lambda*T),0,T)))
}
# Etape 1 : simu Poisson process sous H0
ppH0=PoissonProcess(lambda0,Ti)
ppH0
length(ppH0)
# Etape 2 : creation d'un segment sous H1
tau= 2.5 # longeur de l'intervalle modifie, a fortiori tau < Ti
tau= 3 # longeur de l'intervalle modifie, a fortiori tau < Ti
ppH1.segt=PoissonProcess(lambda1,tau)
ppH1.segt
length(ppH1.segt)
# Etape 3 : insertion du segment dans la sequence H0
dbt=runif(1,0,Ti-tau) # choix de l'indice de temps ou va commencer le segment modifie
dbt
dbt=runif(1,0,Ti-tau) # choix de l'indice de temps ou va commencer le segment modifié
ppH0bis=PoissonProcess(lambda0,Ti)
ppH1.repo=dbt+ppH1.segt # repositionnement des observations dans le temps
ppH1.repo
ppH0_avant=ppH0[which(ppH0<ppH1.repo[1])]
ppH0_apres=ppH0[which(ppH0>ppH1.repo[length(ppH1.repo)])]
ppH0_avant=ppH0bis[which(ppH0bis<ppH1.repo[1])]
ppH0_apres=ppH0bis[which(ppH0bis>ppH1.repo[length(ppH1.repo)])]
ppH1=c(ppH0_avant,ppH1.repo,ppH0_apres)
ppH1
length(ppH1)
#time between events
n1=length(ppH1)
tbe1=ppH1[2:n1]-ppH1[1:n1-1]
tbe1=c(0,tbe1)
n0=length(ppH0)
tbe0=ppH0[2:n0]-ppH0[1:n0-1]
tbe1=c(0,tbe1)
tbe1
list1=data.frame(ProcessusPoissonH1=ppH1,
TimeBetweenEventH1=tbe1)
list1
tbe0=c(0,tbe0)
tbe0
list0=data.frame(ProcessusPoissonH0=ppH0,
TimeBetweenEventH0=tbe0)
list0
poisson=list0[,1]
poisson
list0
list1
```
```{r}
lambda=2
Tps=10
tau=1
pp=PoissonProcess(lambda,Tps)
pp
n=length(pp)
n
which(pp>(Tps-tau))
stop=n-length(which(pp>(Tps-tau)))
stop
ScanStat=0
for (i in (1:stop)) {
cat('\n i=',i)
cat('\t ppi=',pp[i])
x=which((pp>=pp[i])&(pp<=(pp[i]+tau)))
x
cat('\t which=',x)
scan=length(x)
cat(' scan=',scan)
if (scan>ScanStat) ScanStat=scan
}
ScanStat
```
Import data of rainfall in France every 3 hours.
```{r}
Rain_Dataset = read.csv("data/synop.202202.csv", sep = ";")