Geodesic
Order statistics and $(r,s)$-entropy measures
Applications of Mathematics, Tome 39 (1994) no. 5, pp. 321-337
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K. M. Wong and S. Chen [9] analyzed the Shannon entropy of a sequence of random variables under order restrictions. Using $(r,s)$-entropies, I. J. Taneja [8], these results are generalized. Upper and lower bounds to the entropy reduction when the sequence is ordered and conditions under which they are achieved are derived. Theorems are presented showing the difference between the average entropy of the individual order statistics and the entropy of a member of the original independent identically distributed (i.i.d.) population. Finally, the entropies of the individual order statistics are studied when the probability density function (p.d.f.) of the original i.i.d. sequence is symmetric about its mean.
K. M. Wong and S. Chen [9] analyzed the Shannon entropy of a sequence of random variables under order restrictions. Using $(r,s)$-entropies, I. J. Taneja [8], these results are generalized. Upper and lower bounds to the entropy reduction when the sequence is ordered and conditions under which they are achieved are derived. Theorems are presented showing the difference between the average entropy of the individual order statistics and the entropy of a member of the original independent identically distributed (i.i.d.) population. Finally, the entropies of the individual order statistics are studied when the probability density function (p.d.f.) of the original i.i.d. sequence is symmetric about its mean.
DOI : 10.21136/AM.1994.134262
Classification : 62B10, 62G30, 94A15
Keywords: unified $(r, s)$-entropy measure; order statistics; Shannon entropy; logistic distribution. 
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Esteban, M. D.; Morales, D.; Pardo, L.; Menéndez, M. L. Order statistics and $(r,s)$-entropy measures. Applications of Mathematics, Tome 39 (1994) no. 5, pp. 321-337. doi: 10.21136/AM.1994.134262

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