Characterization of order statistics in two runs using conditional expectation

Article type: Research Article

Authors: Kazemi, M.R.^a | Jafari, A.A.^{b; *}

Affiliations: [a] Department of Statistics, Fasa University, Fasa, Iran | [b] Department of Statistics, Yazd University, Yazd, Iran

Correspondence: [*] Corresponding author: A.A. Jafari, Department of Statistics, Yazd University, Yazd, Iran. E-mail:[email protected]

Abstract: The runs test is a well-known test that is used for checking independence between elements of a sample data sequence. Some of runs tests are based on the longest run and others based on the total runs. In this paper, we consider order statistics of two runs statistics, and obtain their probability mass functions. In addition, the means and variances of the order statistics are derived using traditional conditional expectation.

Keywords: Nonparametric statistics, order statistic, permutation, run

DOI: 10.3233/MAS-150356

Journal: Model Assisted Statistics and Applications, vol. 11, no. 2, pp. 99-108, 2016