Expectation Maximization using a Poisson likelihood function

Question

I am trying to apply the expectation-maximization algorithm to estimate missing count data but all the packages in R, such as missMethods, assume a multivariate Gaussian distribution. How would I apply the expectation-maximization algorithm to estimate missing count data assuming a Poisson distribution?

Say we have data that look like this:

x <- c(100,  96,  79, 109, 111,  NA,  93,  95, 119,  90, 121,  96,  NA,  
       NA,  85,  95, 110,  97,  87, 104, 101,  87,  87,  NA,  89,  NA, 
       113,  NA,  95,  NA, 119, 115,  NA, 105,  NA,  80,  90, 108,  90,  
       99, 111,  93,  99,  NA,  87,  89,  87, 126, 101, 106)

Applying impute_EM using missMethods (missMethods::impute_EM(x, stochastic = FALSE)) gives an answer but the data are not continuous but discrete.

I understand that questions like these require a minimum, reproducible example, but I honestly do not know where to start. Even suggested reading to point me in the right direction would be helpful.