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rnormal-distributionmle

R - Calculate MLE of combined distribution

I have a given dataset with 1000 values, which is a combination of two normal distributions N(y1,1) and N(y2,1). The density looks like the following:

enter image description here

I want to calculate the portion of N(y1,1) and N(y2,1) in the dataset and the two means y1 and y2. This is my current approach:

z <- #Dataset as vector with 1000 entries#
lik <- function(mu1, mu2, part) -sum(part*dnorm(z, mu1, 1, log=TRUE) + (1-part)*dnorm(z, mu2, 1, log=TRUE))
mle <- mle(lik, start=list(mu1=-7, mu2=5, part=0.33))

But this gives me the following error message:

Error in solve.default(oout$hessian) : 
    Lapack routine dgesv: system is exactly singular: U[1,1] = 0
Solution

  • I redefined the likelihood to use log() instead of argument log = TRUE.

    Oddly enough, the following works in spite of the warnings. Note that they are warnings, not errors.

    library(stats4)

set.seed(7850)    # Make the results reproducible
z <- sample(c(rnorm(333, -7, 1), rnorm(667, 5, 1)))

plot(density(z))

lik2 <- function(mu1, mu2, part) -sum(log(part*dnorm(z, mu1, 1) + (1-part)*dnorm(z, mu2, 1)))
mle2 <- mle(lik2, start = list(mu1 = -6, mu2 = 6, part = 1/2))
#Warning messages:
#1: In log(part * dnorm(z, mu1, 1) + (1 - part) * dnorm(z, mu2, 1)) :
#  NaNs produced
#2: In log(part * dnorm(z, mu1, 1) + (1 - part) * dnorm(z, mu2, 1)) :
#  NaNs produced
#3: In log(part * dnorm(z, mu1, 1) + (1 - part) * dnorm(z, mu2, 1)) :
#  NaNs produced
#4: In log(part * dnorm(z, mu1, 1) + (1 - part) * dnorm(z, mu2, 1)) :
#  NaNs produced

mle2
#
#Call:
#mle(minuslogl = lik2, start = list(mu1 = -6, mu2 = 6, part = 1/2))
#
#Coefficients:
#       mu1        mu2       part 
#-7.1091780  4.9377339  0.3330038