The Distribution of an Index of Dissimilarity for Two Samples from a Uniform Population ()
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.
Share and Cite:
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.
Conflicts of Interest
The authors declare no conflicts of interest.
References
[1]
|
C. Gini, “Di Una Misura Della Dissomiglianza tra Due Gruppi di Quantità e Delle Sue Applicazioni Allo Studio Delle Relazioni Statistiche,” Proceedings of the R. Vene tian Institute of Sciences, Literatures and Arts, Vol. 74, 1914, pp. 185-213.
|
[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
|