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I am calculating transition probability matrix (TPM) using hmmestimate command of MATALB. The simple vector a=[ 1 1 1 1 3 3 3 2 1 3] and for this the TPM is

hmmestimate(a,a)

ans =
0.6000         0    0.4000
1.0000         0         0
     0    0.3333    0.6667

I believe it is calculated as : (1,3) element:

(# of 1->3 transitions)/(total # of 1) = 2/5 = 0.4

Same rule follows for all the elements. Then why not for element (3,2) and (3,3). For example: (3,2) element:

(# of 3->2 transitions)/(total # of 3) = 1/4 = 0.25 

but the transition matrix calculated by MATLAB entry 0.33. For (3,3), according to my calculation the entry should have been (2/4)=0.5 but it is 0.6667

What am I missing?

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1 Answer 1

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You can't include the $3$ on the end in the count of $3$s because it has no successor. If you have $n$ values, there are only $n-1$ transitions.

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