Journal of Statistical Planning and Inference 76 (1999) 185–201 Random selection in ranked set sampling and its applications Dayong Li a , Bimal K. Sinha b; ∗ , Francois Perron c; 1 a Medex Clinical Trial Services, Inc., Ardmore, PA 19003, USA b Department of Mathematics and Statistics, University of Maryland Baltimore County, Baltimore, MD 21228, USA c Department of Mathematics and Statistics, University of Montreal, Montreal, Canada Received 20 June 1997; accepted 9 June 1998 Abstract The notion of ranked set sampling (RSS) for estimating the mean of a population and its advantage over the use of a simple random sampling for the same purpose are well known. In this paper we provide a new perspective of RSS via the notion of random selection, and discuss some special features of this improved procedure. c  1999 Elsevier Science B.V. All rights reserved. Keywords: Exponential distribution; Logistic distribution; Normal distribution; Random selection; Ranked set sample; Simple random sample 1. Introduction The concept of ranked set sampling (RSS), due originally to McIntyre (1952), for estimating the mean of a population and its advantages over the use of simple random sampling (SRS) for the same purpose are well known (McIntyre, 1952; Takahasi and Wakimoto, 1968; Dell, 1969; Sinha et al., 1996). Many variations of RSS for para- metric estimation have also been recently proposed (Sinha et al., 1996). An RSS of size n is usually obtained by repeatedly selecting n units from a population, n times, and identifying the unit which hopefully provides the smallest, second smallest, and eventually the largest measurement from the n units selected, respectively. Thus, it requires a collection of n 2 units in n batches of n units each and measurement of a total of n units, one from each batch, in a very special way. This can be represented as shown in Table 1. * Corresponding author. E-mail: sinha@umbc2.umbc.edu. 1 Research supported by a grant from the Natural Sciences and Engineering Research Council of Canada. 0378-3758/99/$ – see front matter c  1999 Elsevier Science B.V. All rights reserved. PII: S0378-3758(98)00136-0