asymetrie a gauche

fs = function(x,epsilon,delta) dnorm(sinh(delta*asinh(x)-epsilon))*delta*cosh(delta*asinh(x)-epsilon)/sqrt(1+x^2)
x = seq(-5,5,length=10000)
#plot(x,fs(x,0,1),type="l",ylim=c(0,0.5), xlab="Valeurs de x",ylab="Densité de probabilité")
syme=density(fs(x,-0.8,-1))
n <- length(syme$y)                       #$
dx <- mean(diff(syme$x))                  # Typical spacing in x $
y.unit <- sum(syme$y) * dx                # Check: this should integrate to 1 $
dx <- dx / y.unit                         # Make a minor adjustment
x.mean <- sum(syme$y * syme$x) * dx
y.mean <- syme$y[length(syme$x[syme$x < x.mean])] #$
x.mode <- syme$x[i.mode <- which.max(syme$y)]
y.mode <- syme$y[i.mode]                  #$
y.cs <- cumsum(syme$y)                    #$
x.med <- syme$x[i.med <- length(y.cs[2*y.cs <= y.cs[n]])] #$
y.med <- syme$y[i.med]                                    #$
#
# Plot the density and the statistics.
#
plot(syme, xlim=c(-0.2,0.2), type="l", col="green", xlab="valeur de x", main="Asymétrie à gauche")
temp <- mapply(function(x,y,c) lines(c(x,x), c(0,y), col=c), 
               c(x.mean, x.med, x.mode), 
               c(y.mean, y.med, y.mode), 
               c("Blue", "Gray", "Red"))