A nonparametric test for the two-sample problem based on order statistics

Fazil Aliev, Levent Özbek, Mehmet Fedai Kaya, Coşkun Kuş, Hon Keung Tony Ng and Haikady N. Nagaraja

Communications in Statistics - Theory and Methods, 2024, vol. 53, issue 10, 3688-3712

Abstract: We study a nonparametric test procedure based on order statistics for testing the null hypothesis of equality of two continuous distributions. The exact null distribution of the proposed test statistic is obtained using an enumeration method and a novel combinatorial argument. A recurrence relation for the probability generating function and a sequential approach for computing the mean and variance of the distribution are given. Critical values and characteristics of the distribution for selected small sample sizes are presented. For the Lehmann alternative family, the exact power function of the new test is derived, and its power performance is examined. We also study the power performance of the proposed test under the location-shift and scale-shift alternatives using Monte Carlo simulations and observe its superior performance when compared to commonly used nonparametric tests under various scenarios. A generalization of the proposed procedure for unequal sample sizes is discussed. An illustrative example and some concluding remarks are provided.

Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://hdl.handle.net/10.1080/03610926.2022.2161310 (text/html)
Access to full text is restricted to subscribers.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:taf:lstaxx:v:53:y:2024:i:10:p:3688-3712

Ordering information: This journal article can be ordered from
http://www.tandfonline.com/pricing/journal/lsta20

DOI: 10.1080/03610926.2022.2161310

Access Statistics for this article

Communications in Statistics - Theory and Methods is currently edited by Debbie Iscoe

More articles in Communications in Statistics - Theory and Methods from Taylor & Francis Journals
Bibliographic data for series maintained by Chris Longhurst ().