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The Distribution of an Index of Dissimilarity for Two Samples from a Uniform Population

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DOI: 10.4236/am.2013.47140    3,125 Downloads   4,278 Views   Citations

ABSTRACT

In this paper the authors study the sample behavior of the Gini’s index of dissimilarity in the case of two samples of equal size drawn from the same uniform population. The paper present the analytical results obtained for the exact distribution of the index of dissimilarity for sample sizes n 8. This result was obtained by expressing the index of dissimilarity as a linear combination of spacings of the pooled sample. The obtained results allow to achieve the exact expressions of the moments for any sample size and, therefore, to highlight the main features of the sampling distributions of the index of dissimilarity. The present study can enhance inferential statistical aspects about one of the main contributions of Gini.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

G. Girone and A. Nannavecchia, "The Distribution of an Index of Dissimilarity for Two Samples from a Uniform Population," Applied Mathematics, Vol. 4 No. 7, 2013, pp. 1028-1037. doi: 10.4236/am.2013.47140.

References

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[2] C. Gini, “La Dissomiglianza,” Metron, Vol. 24, No. 1-4, 1965, pp. 85-215.
[3] A. Forcina and G. Galmacci, “Sulla Distribuzione Dell’ Indice Semplice di Dissomiglianza,” Metron, Vol. 32, No. 1-4, 1974, pp. 361-378.
[4] A. Herzel, “Il Valor Medio e la Varianza Dell’Indice Semplice di Dissomiglianza Negli Universi dei Campioni Bernoulliano ed Esaustivo,” Library of Metron, Series C, Notes and Reports, Vol. 2, 1963, pp. 199-224.
[5] S. Bertino, “Sulla Media e la Varianza Dell’Indice Sem plice di Dissomiglianza Nel Caso di Campioni Proven ienti da una Stessa Variabile Casuale Assolutamente Con tinua,” Metron, Vol. 30, No. 1-4, 1972, pp. 256-281.
[6] W. F. Huffer and C. T. Lin, “Spacings, Linear Combinations of,” In: Encyclopedia of Statistical Sciences, John Wiley & Sons Inc., New York, 2006, pp. 7866-7875. doi:10.1002/0471667196.ess5049.pub2

  
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