Mixture of three Gaussian distributions
What will change if we incorporate another distribution into our simulation? You will see that increasing the number of components will spread the mass density to include the extra distribution, but the logic still follows from the previous exercise.
This exercise is part of the course
Mixture Models in R
Exercise instructions
- Create
assignments
, which takes the values 0, 1 and 2 with a probability of 0.3, 0.4 and 0.3, respectively. - The data frame
mixture
samples from a Gaussian with amean
of 5 andsd
of 2, whenassignments
is 1. Ifassignments
is 2, themean
is 10 andsd
is 1. Otherwise, is a standard normal distribution. - Plot the histogram with 50 bins.
Hands-on interactive exercise
Have a go at this exercise by completing this sample code.
number_observations <- 1000
# Create the assignment object
assignments <- sample(
c(0,1,2), size = number_observations, replace = TRUE, prob = c(0.3, ___, 0.3)
)
# Simulate the GMM with 3 distributions
mixture <- data.frame(
x = ifelse(___ == 1, rnorm(n = number_observations, mean = ___, sd = ___), ifelse(assignments == 2, rnorm(n = number_observations, mean = ___, sd = ___), rnorm(n = ___)))
)
# Plot the mixture
mixture %>%
ggplot() + ___(aes(x = x, y = ..density..), ___ = ___)