Moments and Inferences based on Generalized Order Statistics from Benktander Type II Distribution

  • Zaki Anwar Aligarh Muslim University (Women’s College), Aligarh (202002), India
  • Zakir Ali Aligarh Muslim University, Aligarh (202002), India
  • Mohd Faizan Aligarh Muslim University, Aligarh (202002), India
  • Iftkhar Khan Aligarh Muslim University, Aligarh (202002), India
DOI: https://doi.org/10.19139/soic-2310-5070-2001
Keywords: Generalized order statistics (gos), record values, order statistics, single moments, recurrence relations, Benktander Type II distribution, characterization and Maximum likelihood estimator

Abstract

In this paper, we employ generalized order statistics to investigate the moment properties of the Benktander Type II distribution. Through this approach, we derive precise and explicit formulas for single moments and establish recurrence relations for single and product moments. Additionally, we present a characterization of the Benktander Type II distribution, accompanied by further implications regarding moments of record values and ordinary order statistics. We estimate the unknown parameters of the Benktander Type II distribution using Maximum Likelihood (ML) estimation for generalized order statistics (gos). Subsequently, we conduct simulation studies encompassing order statistics. The efficacy of the obtained ML estimates is evaluated through comprehensive simulation analyses, focusing on various moments and their relative mean squared errors. This research contributes to understanding the Benktander Type II distribution's properties and provides valuable insights into its parameter estimation using generalized order statistics.
Published
2025-01-29
How to Cite
Anwar, Z., Ali, Z., Faizan, M., & Khan, I. (2025). Moments and Inferences based on Generalized Order Statistics from Benktander Type II Distribution. Statistics, Optimization & Information Computing, 13(3), 1299-1319. https://doi.org/10.19139/soic-2310-5070-2001
Issue
Vol 13 No 3 (2025)
Section
Research Articles
Authors who publish with this journal agree to the following terms:

    1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
    2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
    3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).