paul-corbalan
/
Scan-Statistics-Project-4Y-INSA
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Update_theoretical_score_distribution.rmd

This commit is contained in:
elisaduz 2022-04-12 10:11:41 +02:00
parent b0dd092c34
commit 2e441a9d11
1 changed files with 103 additions and 18 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

121
Dataset_study.rmd
View File

@ -333,6 +333,41 @@ p
```
```{r}
# Vérification de la distribution theorique des scores
T=10
E=1
lambda0
lambda1
## Choix du E
maxXk = floor(E*(log(lambda1/lambda0)))
while (maxXk < 3) {
E = E+1
maxXk = floor(E*(log(lambda1/lambda0)))
}
E
## Calcul score max
score_max=floor(E*log(lambda1/lambda0))
score_max
## Calcul score_min
score_min_c=floor(E*log(lambda1/lambda0)+E*(lambda0-lambda1)*T)
l=seq(score_min_c,score_max,1)
borne_inf=(l-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
borne_sup=(l+1-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
proba.l=pexp(rate=lambda0,borne_inf)-pexp(rate=lambda0,borne_sup)
proba.l
S=sum(proba.l)
new.proba.s=proba.l/S
new.proba.s
barplot(new.proba.s)
```
```{r}
library(stringr)
@ -348,34 +383,44 @@ workpath = "."
E=1
lambda0=5
lambda1=0.1
max=0
lambda0=2
lambda1=3
while (exp(-lambda0*max) > 10^(-9)){
max = max + 1
}
max
# en fonction de lambda0 tq P(Expo(lambda
#0)>=max)<10^-9
t=seq(0,max,0.1)
probaseuilmin = 10^-9
x=floor(E*log(lambda1/lambda0)+E*(lambda0-lambda1)*t)
head(x)
range(x)
# Vérification de la distribution theorique des scores
E=1
lambda0
lambda1
maxXk = floor(E*(log(lambda1/lambda0)))
while (maxXk < 3) {
E = E+1
maxXk = floor(E*(log(lambda1/lambda0)))
}
E
score_max=floor(E*log(lambda1/lambda0))
score_max
l=-50
borne_inf=(l-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
borne_sup=(l+1-E*log(lambda1/lambda0))/(E*(lambda0-lambda1))
pexp(rate=lambda0,borne_inf)-pexp(rate=lambda0,borne_sup)
l=seq(-100,score_max,1)
x=floor(E*log(lambda1/lambda0)+E*(lambda0-lambda1)*l)
proba.s=(lambda1/lambda0)*(exp(lambda0/(lambda0-lambda1)*(1-l/E))*exp(-lambda0/(E*lambda0-lambda1))-1)
cbind(x,proba.s)
tail(proba.s)
boxplot(proba.s)
sum(proba.s)
s=seq(min(x),max(x),0.1)
s
##tronquer la queue des x (x négatifs)
A=1/(lambda0-lambda1)
B=A*log(lambda1/lambda0)
proba.s=(lambda1/lambda0)*(exp(lambda0/(lambda0-lambda1)*(1-t/E))*exp(-lambda0/(E*lambda0-lambda1))-1)
score_min_c=floor(E*log(lambda1/lambda0)+E*(lambda0-lambda1)*max)
somme=(lambda1/lambda0)*(exp(-lambda0/(E*(lambda0-lambda1))-1))* exp(lambda0/(lambda0-lambda1))*exp(lambda0/(E*(lambda0-lambda1))*(1-score_min_c))/(1-exp(lambda0/(E*(lambda0-lambda1))))
somme=(lambda1/lambda0)*(exp(-lambda0/(E*(lambda0-lambda1)))-1)* exp(lambda0/(lambda0-lambda1))*exp(lambda0/(E*(lambda0-lambda1))*(1-score_min_c))/(1-exp(lambda0/(E*(lambda0-lambda1))))
#proba.s = proba.s/sum(proba.s)
proba.s= proba.s/(1-somme)
@ -422,6 +467,46 @@ write.table(proba.s, file = fichier_proba)
#prob.X = read.table(fichier_proba)
```
```{r}
PoissonProcess <- function(lambda,T) {
return(sort(runif(rpois(1,lambda*T),0,T)))
}
lambda0=2
lambda1=3
Ti=100000
pp1=PoissonProcess(lambda1,Ti)
print(pp1)
n1=length(pp1)
tbe1=pp1[2:n1]-pp1[1:n1-1]
tbe1
ks.test(tbe1,'exp')
x=log(lambda1/lambda0)+(lambda0-lambda1)*tbe1 # ne pas mettre le floor ni le E (certes égale à 1)
hist(x)
summary(x)
# Calcul du maximum des scores
E=1
# THEO à faire !!! max.s=log(lambda1/lambda0)
maxXk = floor(E*(log(lambda1/lambda0)))
maxXk
while (maxXk < 3) {
E = E+1
maxXk = floor(E*(log(lambda1/lambda0)))
}
E
x=floor(E*(log(lambda1/lambda0)+(lambda0-lambda1)*tbe1))
dist.emp.scores=table(x)/sum(table(x))
dist.emp.scores
hist(x)
range(x)
x.verif=seq(range(x)[1],range(x)[2],1)
#dist.theo.scores=lambda0*exp(-lambda0*(A*x.verif-B))
#dist.theo.scores
dist.emp.scores
```
```{r}
barplot(proba.s)