Una generalizzazione della distanza di Cayley per l’analisi dei ranghi
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In this paper we consider the Cayley’s distance for rank data and a generalization that we are going to introduce. The Cayley’s distance is drawn by the number of the inversions in the permutation function derived composing ranking and ordering functions, while the generalized distance comes from a monotonic non decreasing transformation of the previous one. The generalized distance is then used to define the center and the spread of a data set. The important concepts of total and relative disorder are also introduced as measures that seem useful to cluster and to analyze the respondents’ behaviour in either full and partial ranking. An application to the Diaconis’ data-set is shown.
Keywords: Ranking, Ordering, Inversions, Cayley’s distance, Disorder. Author biographyAride Mazzali, Dipartimento Metodi Quantitativi – Università degli Studi di Brescia – Cda Santa Chiara, 50, 25122 BRESCIA (e-mail: mazzali@eco.unibs.it). |