CODEWITHSUNDEEP
rstatistics
Statuser123
Statuser123

Reputation: 83

How to use R for a log-likelihood function with density f being a mixture?

Consider the density f arining from a mixture f(x) = πf1(x) + (1 − π)f2(x) where f1 ∼ N(0, 1) and f2 ∼N(μ,1). Write an R function for the log-likelihood function of the parameter (π, μ) that takes as input a vector of observations x from f

I know that to incorporate f(x) into the log function, you use the dnorm function to get f1 and f2. 

f1 = dnorm(x, 0, 1)
f2 = dnorm(x, u, 1)

and then we would do 

LL=sum(log(f(x))

But overall I am unsure how to actually execute this problem. Any help would be greatly appreciated. Thanks!

Upvotes: 1

Views: 223

Answers (1)

ThomasIsCoding
ThomasIsCoding

Reputation: 101024

From the link https://stephens999.github.io/fiveMinuteStats/intro_to_em.html, I guess you might have already know how to construct the log-likelihood function.

Below is an example that might work for your goal

f <- function(X,p,u) sum(log(p*dnorm(X,0,1) + (1-p)*dnorm(X,u,1)))

Upvotes: 1

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