# Is zero a frequency?

1. Mar 30, 2010

### 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.

2. Mar 30, 2010

### mathman

Lim (x->0) of xlog(x) = 0, for any base.
{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9719369411468506, "perplexity": 1028.4788538246623}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591837.34/warc/CC-MAIN-20180720213434-20180720233434-00559.warc.gz"}