Fit a mixture of normal and lognormal distribution

x.1 <-rnorm(6000, 2.4, 0.6) 
x.2 <-rlnorm(10000, 1.3,0.1) 
 
X <-c(x.1, x.2) 
hist(X,100,freq=FALSE, ylim=c(0,1.5)) 
lines(density(x.1), lty=2, lwd=2) 
lines(density(x.2), lty=2, lwd=2) 
lines(density(X), lty=4) 
 
fitnormlnorm <-function(par, val) { 
  p  <- 1/(1+exp(-par[5])) 
  return(-sum(log(p*dnorm(val, par[1], abs(par[2]), log = FALSE)+ 
                    (1-p)*dlnorm(val, par[3], abs(par[4]), log = FALSE)))) 
} 
 
# Mean 1 
m1=2.3; s1=0.5 
# Mean 2 
m2=1.3; s2=0.1 
# proportion of 1 - logit transform 
p=0 
 
par <-c(m1, s1, m2, s2, p) 
 
result2 <-optim(par, fitnormlnorm, method="BFGS", val=X,  
               hessian=FALSE, control=list(trace=1)) 
 
lines(seq(from=0, to=5, length=100),  
      dnorm(seq(from=0, to=5, length=100),  
            result2$par[1], result2$par[2]), col="red") 
 
lines(seq(from=0, to=5, length=100),  
      dlnorm(seq(from=0, to=5, length=100),  
             result2$par[3], result2$par[4]), col="green") 
 
p  <- 1/(1+exp(-result2$par[5])) 
 
paste("Proportion of Gaussian data",  p) 
 
lines(seq(from=0, to=5, length=100),  
      p*dnorm(seq(from=0, to=5, length=100),  
             result2$par[1], result2$par[2])+ 
        (1-p)*dlnorm(seq(from=0, to=5, length=100),  
                    result2$par[3], result2$par[4]), col="blue") 


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