Citations From References: 2 From Reviews: 1 MR1052779 (91c:94014) 94A17 Wong, Kon M. (3-MMAS-E) ; Chen, Shuang (3-MMAS-E) The entropy of ordered sequences and order statistics. IEEE Trans. Inform. Theory 36 (1990), no. 2, 276–284. Let x =(x 1 , ··· ,x n ) be a sequence of random variables and y =(y 1 , ··· ,y n ) be the corresponding order statistic. Suppose J is the ensemble of the ordering index se- quence. Let H (v) denote the Shannon entropy of the random variable v and let H (y)= n -1 ∑ n i=1 H (y i ). Regardless of the underlying distribution, it is shown that (1) 0 ≤ H (x) − H (y)= H (J ) ≤ log n!; (2) if the x i ’s are i.i.d. then 0 ≤ H (x) − H (y)= c n , where c n is an increasing function of n only; (3) if the x i ’s are i.i.d. from a distribution which is symmetric about its mean then H (y i ) is symmetric about the median. The proofs of these results are very simple. One should wonder about the reduction in entropy due to ordering even though the order statistic y is a suﬃcient statistic and one should expect that the Shannon entropy is not the right measure of entropy. Adnan M. Awad c  Copyright American Mathematical Society 1991, 2015 Citations From References: 0 From Reviews: 0 MR1032592 (90m:94029) 94A17 60F05 62B10 Zografos, K. (GR-IOAN) ; Ferentinos, K. [Ferentinos, Kosmas K.] (GR-IOAN) ; Papaioannou, T. (GR-IOAN) Limiting properties of some measures of information. Ann. Inst. Statist. Math. 41 (1989), no. 3, 451–460. This paper extends some well-known results about the limiting behaviour of the Kullback-Leibler and the Matusita information measures to the Csisz´ ar, R´ enyi and Fisher information measures. The proofs are parallel to those given by Kullback. A new criterion of convergence in distribution based on the convergence of the Csisz´ ar and R´ enyi measures of information is given. The problem about the convergence of the Fisher information, being equivalent to the convergence in distribution, is left open. Adnan M. Awad c  Copyright American Mathematical Society 1990, 2015 Citations From References: 0 From Reviews: 0