I am wanting to apply a Hidden Markov Model (HMM) to a data set of fishing vessel speeds. I'm struggling a bit to get started because as I understand it i need to know how many distributions (inferred states) are in my observed data parameter (in this case speed) by finding the number of distributions m=1,2,3,4 etc using maximum likelihood. At the moment i am wanting to model the most likely number of states for a single vessel. Below is the observed speed for one fishing trip. I also don't know what type of distributions are making up the mixture - which seems to impact how you model the mixture?
df$SP <- c(11.43,10.75,9.87,8.09,0.00,10.34,10.57,9.93,9.76,10.44,3.18,3.55,1.18,5.55,3.43,3.65,9.60,0.00,0.00,3.18,3.92, 2.89,1.01,1.92,2.97,3.47,2.81,3.65,7.00,7.08,4.66,4.64,0.00,0.50,3.41,5.55,3.40,1.51,5.47,2.85,3.80,3.12,4.33,2.99,3.98,0.00,0.00,3.40,10.46,10.46,11.76,10.15,10.07)