Is Zero a Frequency? Miller G.A, Frick F.C. Statistical Behavioristics 1949

[EasilyConfuse]

I've been playing with an equation that purports to provide a measure of sequence variability
Miller G.A, Frick F.C. Statistical behavioristics and sequences of responses. Psychological Review. 1949;56:311–324

If a person is asked to produce a sequence of responses and there are say 16 possible sequences the statistic is

-∑_(i=1)^16 ([RF)_i*log_2 (RF_i)])/(log_2 (16)) , where 16 equals the number of possible sequences and RFi is the relative frequency of any given sequence.

1 mean they've produced each sequence equally often, and zero that they've produced just one sequence.

So here's my problem, if someone doesn't produce a particular sequence I'm then faced with the conundram do I use a relative frequency of zero? If I do I'm then faced with the problem of trying to calculate log base 2 of zero and also multiply that by zero in the numerator - the solution to this is indeterminate and I can't solve it. So either I ignore sequences that weren't produced when summing across relative frequencies - if I do then I can avoid trying solve for log 2 (0), and I can solve this problem - or at least get estimates of U that are bigger when . But this seems very inelegant. Any thoughts on this would be helpful.

 

[mathman]

Lim (x->0) of xlog(x) = 0, for any base.