I fitted a gaussian mixture to my financial data. The data can be found here: http://uploadeasy.net/upload/32xzq.rar I look at the density with plot(density(dat),col="red",lwd=2) this has a skew of library(e1071) skewness(dat) -0.1284311 Now, I fit a gaussian mixture according to: f(l)=πϕ(l;μ1,σ21)+(1−π)ϕ(l;μ2,σ22) with: datnormalmixturegaussian<-normalmixEM(dat,lambda=c(0.3828,(1-0.3828)),k=2,fast=TRUE) save the values with: pi<-datnormalmixturegaussian$lambda[1] mu1<-datnormalmixturegaussian$mu[1] mu2<-datnormalmixturegaussian$mu[2] sigma1<-datnormalmixturegaussian$sigma[1] sigma2<-datnormalmixturegaussian$sigma[2] the values are: pi = 0.383 mu1= -0.00089 mu2= 0.00038 sigma1= 0.0123 sigma2= 0.02815 Plot the single densities and the mixture: plot.new() xval<-seq(-0.06,0.06,length=1000) mixturedensity<-pi*dnorm(xval,mu1,sigma1)+(1-pi)*dnorm(xval,mu2,sigma2) plot(xval,mixturedensity,type="l",lwd=2,col="black",cex.axis=1.2,cex.lab=1.2,main="Single univariate normal densities and mixture density",xlab="Loss",ylab="Density",ylim=c(0,36)) curve(dnorm(x,mu1,sigma1),add=TRUE,lty=2,col="darkgreen") curve(dnorm(x,mu2,sigma2),add=TRUE,lty=2,col="blue") legend("topright", legend=c("Mixture density\n","normal distribution\n of stable market regime\n","normal distribution\n of crash market regime\n"), bty = "n",lwd=2, cex=1, col=c("black","blue","darkgreen"), lty=c(1,2,2)) One can see, that both single distributions have a mean of almost zero, wherease one has a high volatility and the other a low volatility. The normal distribution 1, the green one with the high peak has the parameters mu1= -0.00089 and sigma1=0.0123 and occurs (this is pi from output of normalmixEM) with a probability of 0.383. The normal distribution 2 with the smaller peak and the higher volatility has the parameters mu2=0.00038 and sigma2=0.02815 and a probability of 1-0.383. I imagine the generating of the mixture density as follows: We have a distribution which is quite probable (1-0.383) and has mu2=0.00038. If the mixture density is done, we "add" a second distribution which is a bit shifted to the left (this one occurs with a probability of 0.383 and has a negative mean). Since the distribution we add lies a bit more to the left I would expect, that the mixture density has a negative skew, since the left tail of the resulting mixture will be heavier? I control this with: skewness(mixturedensity) which gives a positive skew of 0.7065. Now my question is: Why? I would expect a negative skew, since I thought the mixture density will have a a fatter left tail, since we add to the probable distribution with positive mean a second distribution which is a bit shifted to the left? [[alternative HTML version deleted]]