Statistics and Probability Letters 112 (2016) 137–145 Contents lists available at ScienceDirect Statistics and Probability Letters journal homepage: www.elsevier.com/locate/stapro Some results on residual entropy of ranked set samples Saeid Tahmasebi a,∗ , Ali Akbar Jafari b , Maryam Eskandarzadeh a a Department of Statistics, Persian Gulf University, Bushehr, Iran b Department of Statistics, Yazd University, Yazd, Iran article info Article history: Received 26 July 2015 Received in revised form 24 January 2016 Accepted 25 January 2016 Available online 17 February 2016 Keywords: Ranked set sample Residual entropy Residual Rényi entropy abstract In this paper, a number of results are presented for the residual and past entropies of ranked set sample. In addition, some properties are compared with their counterparts in the simple random sample of size n = 2. Finally, a dynamic residual measure of inaccuracy associated with two residual lifetime distributions of ranked set sample and simple random sample is obtained. © 2016 Elsevier B.V. All rights reserved. 1. Introduction McIntyre (1952) first proposed ranked set sampling to estimate the mean pasture yields and indicated that ranked set sampling is a more efficient sampling method in comparison with simple random sampling in terms of the population mean estimation. We assume that X SRS ={X i , i = 1,..., n} denotes a simple random sample (SRS) of size n from a continuous distribution with probability density function (pdf) f and cumulative distribution function (cdf) F . The one-cycle ranked set sampling involves an initial ranking of n samples of size n as follows: 1 : X (1:n)1 X (2:n)1 ··· X (n:n)1 → X (1)1 = X (1:n)1 2 : X (1:n)2 X (2:n)2 ··· X (n:n)2 → X (2)2 = X (2:n)2 . . . . . . . . . . . . . . . . . . . . . n : X (1:n)n X (2:n)n ··· X (n:n)n → X (n)n = X (n:n)n where X (i:n)j denotes the ith order statistic from the jth SRS of size n. The resulting sample is called a ranked set sample (RSS) of size n and denoted by X RSS ={X (i)i , i = 1,..., n}. Here, X (i)i is the ith order statistic in a set of size n obtained from the ith sample with pdf f (i) (x) = n! (i − 1)!(n − i)! f (x)[F (x)] i−1 [1 − F (x)] n−i , and corresponding cdf F (i) (x) is given by F (i) (x) = n  j=i  n j  [F (x)] j [ ¯ F (x)] n−j , ∗ Corresponding author. E-mail addresses: tahmasebi@pgu.ac.ir (S. Tahmasebi), aajafari@yazd.ac.ir (A.A. Jafari), eskandarymaryam@gmail.com (M. Eskandarzadeh). http://dx.doi.org/10.1016/j.spl.2016.01.022 0167-7152/© 2016 Elsevier B.V. All rights reserved.