Recently, Chen and Sbert proposed a general divergence measure. This report presents some interim findings about the question whether the divergence measure is a metric or not. It has been postulated that (i) the measure might be a metric when (0 < k <= 1), and (ii) the k-th root of the measure might be a metric when (k > 1). The report shows that for a 2-letter alphabet, postulation (i) can be proved. The possible pathway for obtaining a proof for (i) in n-letter cases is also discussed. The authors hope that the report may stimulate more scholarly effort to study the mathematical properties of this divergence measure.
翻译:最近,Chen和Sbert提出了一般性差异衡量标准。本报告介绍了关于差异衡量标准是否是衡量标准的问题的一些临时结论。有人假定:(一)当(0 < k ⁇ 1)时,该措施可能是衡量标准,(二)当(k > 1)时,该措施的k-th根可能是衡量标准。报告显示,对于双字母字母字母字母的字母表,(一)可以证明。也讨论了获得(一)n字母中(一)案件证据的可能途径。作者希望报告能够激发更多的学术努力,研究这一差异计量的数学性质。