# Mean and Variance of a Set of Sequences

I am trying to find the probability distribution (like mean and variance) of a set of sequences which have different length. I came into different measurement models that quantify the distance between difference sequences, but I cannot find something on the probability distribution of sequences. Is there anyway to extract the parameters for the distribution of a set of sequences?

There are a series of descriptive statistics of a set of sequences, which you can easily obtain for instance with the TraMineR R package (You find a lot of documentation on http://mephisto.unige.ch/traminer).

Here are a few examples:

• the relative frequency of each distinct sequence pattern;
• the successive cross-sectional state distributions at the successive positions;
• the sequence of cross-sectional entropies (i.e., the diversity of the state at the successive positions)
• longitudinal characteristics for each sequence such as longitudinal entropy, complexity index, ...

With TraMineR you can also compute pairwise dissimilarities, and based on these dissimilarities:

• the medoid (sequence with smallest sum of distances to all other sequences)
• other representative sequences, such as sequence with densest neighborhood.
• discrepancy measure (pseudo variance)

All this is indeed for categorical sequences, for which the mean does not make sense.