Estimating Kappa Distribution Parameters: A Comparative Study of Maximum Likelihood and LQ-Moment Approaches

  • Manal Mohammed Koran
  • Sameera Abdulsalam Othman
  • Delbrin Ahmed
DOI: https://doi.org/10.19139/soic-2310-5070-2149
Keywords: Kappa distributions, maximum likelihood, LQ - momente

Abstract

The Kappa distribution, pioneered by researchers such as Hosking, stands as a widely applied continuous model in diverse scientific fields. This study delves into its practical utility, with a specific focus on amalgamating Gamma and Log-Normal distributions. The vital distributional parameters($\alpha ,\beta,\theta$)are subject to estimation through both Maximum Likelihood (MLE) and LQ-moment methods. Across a spectrum of sample sizes (25, 50,100, and 150), the LQ-moment method consistently exhibits superior performance compared to MLE.Additionally, the research introduces two essential reliability metrics: Mean Inactivity Time (MIT) and Stress-Strength Reliability (SSR). MIT, influenced by distribution parameters, provides insights into the temporal behavior of the random variable. SSR evaluates system reliability by accounting for the probability of component failure under stress conditions. The paper concludes with a comparative analysis of parameter estimation methods, emphasizing the enhanced accuracy of the LQ-moment approach, particularly noticeable in smaller sample sizes (50 and 100).
Published
2025-04-09
How to Cite
Koran, M. M., Othman, S. A., & Ahmed, D. (2025). Estimating Kappa Distribution Parameters: A Comparative Study of Maximum Likelihood and LQ-Moment Approaches. Statistics, Optimization & Information Computing. https://doi.org/10.19139/soic-2310-5070-2149
Issue
Online First
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).