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Valider fa38efcb rédigé par Alain Guillet's avatar Alain Guillet
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Calculs à réaliser par l'app Shiny

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library(shiny)
# library(xtable)
plotzmaxlim=5 #limite max de l'axe des Z
plotzlab="Z~N(0;1)"
linezlab=1
linexlab=3
linemulab=2.5
yt=0.48 #y des textes
xt=-5 #x des textes
ztxt=1.5 #zoom text
txt="" #contenu des textes
z=seq(-4,4,length=200) #détermine les valeurs de z à utiliser : de -4 à 4 créer 200 valeurs et les mettre en vecteur
y=dnorm(z) #créer pour chaque z les équivalents y de la courbe de gauss
#Define server logic required to plot various variables against mpg
shinyServer(function(input, output) {
getInputValues<-reactive({
return(input)#collect all inputs
})
getComputedValues<-reactive({
v<-getInputValues() # get all values of input list
cv<-list()#created empty computed values list
if(v$Tabset!=3){
if(v$Tabset==1){
if(v$sens=="inf"){
cv$z1=-5
cv$z2=round((v$x-v$mx)/v$sx,2)
}
if(v$sens=="sup"){
cv$z2=5
cv$z1=round((v$x-v$mx)/v$sx,2)
}
if(v$sens=="equal"){
cv$z2=round((v$x-v$mx)/v$sx,2)
cv$z1=round((v$x-v$mx)/v$sx,2)
}
}
if(v$Tabset==2){
cv$x1=min(v$x1,v$x2)
cv$x2=max(v$x1,v$x2)
cv$z1=round((cv$x1-v$mx)/v$sx,2)
cv$z2=round((cv$x2-v$mx)/v$sx,2)
}
cv$z1l=ifelse(cv$z1 < -3,-3,cv$z1) # limite la valeur de z à -3 pour le calcul de la position de
cv$z2l=ifelse(cv$z2 > 3,3,cv$z2) # limite la valeur de z à 3 pour le calcul de la position dep
cv$z1lp=ifelse(cv$z1 < -4,-4,cv$z1) # limite la valeur de z à -4 pour le tracé du polugone sinon il overwrite le pointillé
cv$z2lp=ifelse(cv$z2 > 4,4,cv$z2) # limite la valeur de z à 4 pour le tracé du polugone sinon il overwrite le pointillé
cv$xlp=seq(cv$z1lp,cv$z2lp,length=200) #crée une seconde abscisse de -2 à 2
cv$ylp=dnorm(cv$xlp) #crée pour chaque xles équivalent y Normaux
cv$pz1=pnorm(cv$z1,mean=0,sd=1)
cv$pz1r=round(cv$pz1,4)
cv$pz1i=1-cv$pz1
cv$pz1ir=1-cv$pz1r#round(pz1i,4)
cv$pz2=pnorm(cv$z2,mean=0,sd=1)
cv$pz2r=round(cv$pz2,4)
cv$pz2i=1-cv$pz2
cv$pz2ir=1-cv$pz2r#round(pz2i,4)
cv$p=cv$pz2-cv$pz1
cv$pr=cv$pz2r-cv$pz1r#round(p,4)
cv$pp=round(cv$pr*100,0)
if(v$Tabset==1){
if(v$sens=="inf"){
cv$zx=(max(cv$z2l,cv$z1l)-((max(cv$z2l,cv$z1l)-min(cv$z2l,cv$z1l))/3))
}
if(v$sens=="sup"){
cv$zx=(min(cv$z2l,cv$z1l)+((max(cv$z2l,cv$z1l)-min(cv$z2l,cv$z1l))/3))
}
if(v$sens=="equal"){
cv$zx=cv$z2l
}
}
if(v$Tabset==2){
cv$zx=(cv$z2l-(cv$z2l-cv$z1l)/2)
}
}
return(cv)
})
output$zPlot <- renderPlot({
v<-getInputValues()
cv<-getComputedValues()
if(v$Tabset==1){
par(mai=c(1.02,0.8,0.9,1.5)) #marges bottom left top right en inches les valeurs par défaut sont 1 1 1 1
plot(z,y,type="l",lwd=2,col="blue",yaxt="n",bty="n",,las=1,xaxs="i",yaxs="i",cex.lab=1,cex.axis=1.5,xlim=c(-5,plotzmaxlim),ylim=c(0,0.4),xaxp=c(-4,4,8),ylab="density",xlab="")
axis(2,las=2)#col="red",col.axis="blue",font.axis=2
lines(x=c(-4.7,-4),y = c(0,0),lty=2)
lines(x=c(4.7,4),y = c(0,0),lty=2)
polygon(c(cv$z1lp,cv$xlp,cv$z2lp),c(0,cv$ylp,0),col="lightblue") #trace un polygone qui commence à -2;0 puis x;y puis 2;0 et comme c'est polygon il ferme entre 2;0 et -2;0
mtext(plotzlab,side=1,line=1,at=5,cex=ztxt,adj = 0)
for(s in -4:4){#Ecrire valeurs de x sur abscisse
vx=v$mx+s*v$sx
mtext(vx,side=1,line=linexlab,at=s,cex=1.5)
}
mtext(paste("X~N(",v$mx,";",v$sx^2,")",sep=""),side=1,line=linexlab,at=5,cex=1.2,adj = 0)
text(cv$zx,0.1,cv$pr,cex=2)#cex = zoom taille texte
}
})
output$zPlotInt <- renderPlot({
v<-getInputValues()
cv<-getComputedValues()
if(v$Tabset==2){
par(mai=c(1.02,0.8,0.9,1.5)) #marges bottom left top right en inches les valeurs par défaut sont 1 1 1 1
plot(z,y,type="l",lwd=2,col="blue",yaxt="n",bty="n",,las=1,xaxs="i",yaxs="i",cex.lab=1,cex.axis=1.5,xlim=c(-5,plotzmaxlim),ylim=c(0,0.4),xaxp=c(-4,4,8),ylab="density",xlab="")
axis(2,las=2)#col="red",col.axis="blue",font.axis=2
lines(x=c(-4.7,-4),y = c(0,0),lty=2)
lines(x=c(4.7,4),y = c(0,0),lty=2)
polygon(c(cv$z1lp,cv$xlp,cv$z2lp),c(0,cv$ylp,0),col="lightblue") #trace un polygone qui commence à -2;0 puis x;y puis 2;0 et comme c'est polygon il ferme entre 2;0 et -2;0
mtext(plotzlab,side=1,line=1,at=5,cex=ztxt,adj = 0)
for(s in -4:4){#Ecrire valeurs de x sur abscisse
vx=v$mx+s*v$sx
mtext(vx,side=1,line=linexlab,at=s,cex=1.5)
}
mtext(paste("X~N(",v$mx,";",v$sx^2,")",sep=""),side=1,line=linexlab,at=5,cex=1.2,adj = 0)
text(cv$zx,0.1,cv$pr,cex=2)#cex = zoom taille texte
}
})
output$Text <- renderText({
v<-getInputValues()
cv<-getComputedValues()
txt=paste("<p>Si X est une variable al&eacute;atoire Normale X~N(&mu;;&sigma;&sup2;) telle que X~N(",v$mx,";",v$sx^2,") alors Z=(X-&mu;)/&sigma; est aussi une variable al&eacute;atoire Normale de param&egrave;tres Z~N(0;1) ",sep="")
if(v$sens=="inf" & cv$z2>-4 & cv$z2<0){
txt=paste(txt," et P(X&le;x) = P(Z&le;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z2,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&le;",round(cv$z2*v$sx+v$mx,2),") = P(Z&le;",cv$z2,") = 1-P(Z&le;",cv$z2*-1,") = 1-",cv$pz2ir," = ",cv$pz2r,"</p>",sep="")
}
if(v$sens=="inf" & cv$z2<4 & cv$z2>=0){
txt=paste(txt," et P(X&le;x) = P(Z&le;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z2,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&le;",round(cv$z2*v$sx+v$mx,2),") = P(Z&le;",cv$z2,") = ",cv$pz2r,"</p>",sep="")
}
if(cv$z1>-4 & cv$z1<0 & v$sens=="sup"){
txt=paste(txt," et P(X&ge;x) = P(Z&ge;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z1,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&ge;",round(cv$z1*v$sx+v$mx,2),") = P(Z&ge;",cv$z1,") = P(Z&le;",cv$z1*-1,") = ",cv$pz1ir,"</p>",sep="")
}
if(cv$z1<4 & cv$z1>=0 & v$sens=="sup"){
txt=paste(txt," et P(X&ge;x) = P(Z&ge;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z1,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&ge;",round(cv$z1*v$sx+v$mx,2),") = P(Z&ge;",cv$z1,") = 1-P(Z&le;",cv$z1,") = 1-",cv$pz1r," = ",cv$pz1ir,"</p>",sep="")
}
if(v$sens=="inf" & cv$z2>=4){
txt=paste(txt," et P(X&le;x) = P(Z&le;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z2,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&le;",round(cv$z2*v$sx+v$mx,2),") = P(Z&le;",cv$z2,") = P(Z&le;&infin;) = ",cv$pz2r,"</p>",sep="")
}
if(v$sens=="inf" & cv$z2<=-4){
txt=paste(txt," et P(X&le;x) = P(Z&le;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z2,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&le;",round(cv$z2*v$sx+v$mx,2),") = P(Z&le;",cv$z2,") = 1-P(Z&le;",cv$z2*-1,") = 1-P(Z&le;&infin;) = 1-1 = ",cv$pz2r,"</p>",sep="")
}
if(cv$z1<=-4 & v$sens=="sup"){
txt=paste(txt," et P(X&ge;x) = P(Z&ge;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z1,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&ge;",round(cv$z1*v$sx+v$mx,2),") = P(Z&ge;",cv$z1,") = 1-P(Z&le;",cv$z1*-1,") = 1-P(Z&le;&infin;) = 1-1 = ",cv$pz1r,"</p>",sep="")
}
if(cv$z1>=4 & v$sens=="sup"){
txt=paste(txt," et P(X&ge;x) = P(Z&ge;z).","</p>",sep="")
txt=paste(txt,"<p>Si x=",v$x,", alors z = (x-&mu;)/&sigma; = (",v$x,"-",v$mx,")/",v$sx," = ",v$x-v$mx,"/",v$sx," = ",cv$z1,"</p>",sep="")
txt=paste(txt,"<p>Donc P(X&ge;",round(cv$z1*v$sx+v$mx,2),") = P(Z&ge;",cv$z1,") = 1-P(Z&le;",cv$z1,") = 1-P(Z&le;&infin;) = 1-1 = ",cv$pz1r,"</p>",sep="")
}
if(v$sens=="equal"){
txt=paste(txt," et P(X=x) = P(Z=z) = 0.","</p>",sep="")
}
paste(txt)
})
output$TextInt <- renderText({
v<-getInputValues()
cv<-getComputedValues()
txt=paste("<p>Si X est une variable al&eacute;atoire Normale X~N(&mu;;&sigma;&sup2;) telle que X~N(",v$mx,";",v$sx^2,") alors Z=(X-&mu;)/&sigma; est aussi une variable al&eacute;atoire Normale de param&egrave;tres Z~N(0;1) </p>",sep="")
txt=paste(txt,"<p>P(x<sub>1</sub> &le; X &le; x<sub>2</sub>) = P(z<sub>1</sub> &le; Z &le; z<sub>2</sub>).","</p>",sep="")
txt=paste(txt,"<p>Si x<sub>1</sub>=",v$x1,", alors z<sub>1</sub> = (x<sub>1</sub>-&mu;)/&sigma; = (",v$x1,"-",v$mx,")/",v$sx," = ",v$x1-v$mx,"/",v$sx," = ",cv$z1,"</p>",sep="")
txt=paste(txt,"<p>Si x<sub>2</sub>=",v$x2,", alors z<sub>2</sub> = (x<sub>2</sub>-&mu;)/&sigma; = (",v$x2,"-",v$mx,")/",v$sx," = ",v$x2-v$mx,"/",v$sx," = ",cv$z2,"</p>",sep="")
txt=paste(txt,"<p>Donc P(",cv$x1," &le; X &le; ",cv$x2,") = P(",cv$z1," &le; Z &le; ",cv$z2,") = P(Z &le; ",cv$z1,")-P(Z &le; ",cv$z2,") = ",cv$pz1ir,"-",cv$pz2ir," = ",cv$pr,"</p>",sep="")
paste(txt)
})
output$Table <- renderText({
v<-getInputValues()
if(v$signeZ == "pos"){
rows<-seq(0.0,3.4,by=0.1)
cols<-seq(0.00,0.09,by=0.01)
} else {
rows<-rev(seq(-3.4,-0.0,by=0.1))
cols<-rev(seq(-0.09,0.00,by=0.01))
}
p<-c()
# définir ici table header et faire html code de Table a la main car renderTable force les colsnames en header mais ne permet pas les rownames en header
txt<-'<table cellspacing="0" cellpadding="5" border="0" style="border:1px solid #000;">'
txt<-paste(txt,'<tr style="border-bottom:1px solid #000;"><th style="border-right:1px solid #000;">Z</th>',sep="")
for(j in 1:length(cols)){
txt<-paste(txt,'<th>',format(cols[[j]], nsmall = 2),'</th>',sep="")
}
txt<-paste(txt,'</tr>',sep="")
for(i in 1:length(rows)){
if(i == 11 || i == 21 ){
txt<-paste(txt,'<tr style="border-bottom:1px solid #000;">',sep="")
} else {
txt<-paste(txt,'<tr>',sep="")
}
txt<-paste(txt,'<th style="border-right:1px solid #000;">',format(rows[[i]], nsmall = 1),'</th>',sep="")
for(j in 1:length(cols)){
if(v$sensTable == "inf"){
txt<-paste(txt,'<td>',sprintf("%.4f",round(pnorm(rows[[i]]+cols[[j]]),4)),'</td>',sep="")
} else {
txt<-paste(txt,'<td>',sprintf("%.4f",1-round(pnorm(rows[[i]]+cols[[j]]),4)),'</td>',sep="")
}
}
txt<-paste(txt,'</tr>',sep="")
}
txt<-paste(txt,'</table>',sep="")
paste(txt)
# for(i in 1:length(rows)){
# for(j in 1:length(cols)){
# p<-c(p,round(pnorm(rows[[i]]+cols[[j]]),4))
# }
# }
# m<-matrix(p,length(rows),length(cols),byrow=TRUE)
# d<-data.frame(m)
# rownames(d)<-format(rows, nsmall = 2)
# colnames(d)<-format(cols, nsmall = 2)
# d
})
})
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