Abstract
Given a frequency table \({F=\{f_{jk},(j,k)\in\,J\times K\}}\) crossing two categorical variables J and K, we consider a family of metrics of L p -type on J defined by \({d_J^p (j,j^{\prime}) = \Sigma_k g(f_{.k})|f_{jk}/f_{j.} - f_{j^{\prime}k}/f_{j^{\prime}.}|^p}\), where g is a positive function, and a symmetrical one on K. We investigate under which conditions on g, the famous principle of distributional equivalence is fulfilled by these metrics for every rational or every real F.
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Fichet, B. Metrics of L p -type and distributional equivalence principle. Adv Data Anal Classif 3, 305–314 (2009). https://doi.org/10.1007/s11634-009-0049-4
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DOI: https://doi.org/10.1007/s11634-009-0049-4