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ADVANCED AND APPLIED SCIENCES

EISSN: 2313-3724, Print ISSN: 2313-626X

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 Volume 9, Issue 2 (February 2022), Pages: 104-108

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 Original Research Paper

 Title: Parameter estimate for three-parameter kappa distribution using LH-moments approach

 Author(s): Zahrahtul Amani Zakaria 1, *, Jarah Moath Suleiman Ali 1, Wan Nur Syahidah Wan Yusoff 2

 Affiliation(s):

 1Faculty of Informatics and Computing, Universiti Sultan Zainal Abidin, Kuala Terengganu, Malaysia
 2Centre for Mathematical Sciences, College of Computing and Applied Sciences, Universiti Malaysia Pahang, Pahang, Malaysia

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 * Corresponding Author. 

  Corresponding author's ORCID profile: https://orcid.org/0000-0002-7198-1403

 Digital Object Identifier: 

 https://doi.org/10.21833/ijaas.2022.02.011

 Abstract:

The method of higher-order L-moments (LH-moment) was proposed as a more robust alternative compared to classical L-moments to characterize extreme events. The new derivation will be done for Mielke-Johnson’s Kappa and Three-Parameters Kappa Type-II (K3D-II) distributions based on the LH-moments approach. The data of maximum monthly rainfall for Embong station in Terengganu were used as a case study. The analyses were conducted using the classical L-moments method with 𝜂 = 0 and LH-moments methods with 𝜂 = 1, 𝜂 = 2, 𝜂 = 3 and 𝜂 = 4 for a complete data series and upper parts of the distributions. The most suitable distributions were determined based on the Mean Absolute Deviation Index (MADI), Mean Square Deviation Index (MSDI), and Correlation (𝑟). Also, L-moment and LH-moment ratio diagrams were used to represent visual proofs of the results. The analysis showed that LH-moments methods at a higher order of K3D-II distribution best fit the data of maximum monthly rainfalls for the Embong station for the upper parts of the distribution compared to L-moments. The results also proved that whenever 𝜂 increases, LH-moments reflect more and more characteristics of the upper part of the distribution. This seems to suggest that LH-moments estimates for the upper part of the distribution events are superior to L-moments in fitting the data of maximum monthly rainfalls. 

 © 2022 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

 Keywords: Higher-order moments, L-moments, Probability distribution, Rainfall forecasting

 Article History: Received 27 June 2021, Received in revised form 27 September 2021, Accepted 9 December 2021

 Acknowledgment 

The authors would like to thank the Department of Irrigation and Drainage, Ministry of Natural Resources and Environment, Malaysia for providing the rainfall data and Center for Research Excellence and Incubation Management, Universiti Sultan Zainal Abidin, Malaysia for funding this research.

 Compliance with ethical standards

 Conflict of interest: The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

 Citation:

 Zakaria ZA, Ali JMS, and Yusoff WNSW (2022). Parameter estimate for three-parameter kappa distribution using LH-moments approach. International Journal of Advanced and Applied Sciences, 9(2): 104-108

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 Figures

 Fig. 1

 Tables

 Table 1 Table 2 Table 3   

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 References (20)

  1. Bhat MS, Alam A, Ahmad B, Kotlia BS, Farooq H, Taloor AK, and Ahmad S (2019). Flood frequency analysis of river Jhelum in Kashmir basin. Quaternary International, 507: 288-294. https://doi.org/10.1016/j.quaint.2018.09.039   [Google Scholar]
  2. Bora DJ, Borah M, and Bhuyan A (2017). Regional analysis of maximum rainfall using L-moment and LH-moment: A comparative case study for the northeast India. Mausam, 68(3): 451-462. https://doi.org/10.54302/mausam.v68i3.677   [Google Scholar]
  3. Busababodhin P, Am Seo Y, Park JS, and Kumphon BO (2016). LH-moment estimation of Wakeby distribution with hydrological applications. Stochastic Environmental Research and Risk Assessment, 30(6): 1757-1767. https://doi.org/10.1007/s00477-015-1168-4   [Google Scholar]
  4. Greenwood JA, Landwehr JM, Matalas NC, and Wallis JR (1979). Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form. Water Resources Research, 15(5): 1049-1054. https://doi.org/10.1029/WR015i005p01049   [Google Scholar]
  5. Harun NA, Makhtar M, Aziz AA, Mohamad M, and Zakaria ZA (2017). Implementation of apriori algorithm for a new flood area prediction system. Advanced Science Letters, 23(6): 5419-5422. https://doi.org/10.1166/asl.2017.7390   [Google Scholar]
  6. Hosking JR (1990). L‐moments: Analysis and estimation of distributions using linear combinations of order statistics. Journal of the Royal Statistical Society: Series B (Methodological), 52(1): 105-124. https://doi.org/10.1111/j.2517-6161.1990.tb01775.x   [Google Scholar]
  7. Hosking JR (1994). The four-parameter kappa distribution. IBM Journal of Research and Development, 38(3): 251-258. https://doi.org/10.1147/rd.383.0251   [Google Scholar]
  8. Hosking JRM and Wallis JR (1997). Regional frequency analysis: An approach based on L-moments. Cambridge University Press, Cambridge, UK. https://doi.org/10.1017/CBO9780511529443   [Google Scholar]
  9. MacKenzie CA and Winterstein SR (2011). Comparing L-moments and conventional moments to model current speeds in the North Sea. In the 61st Annual IIE Conference and Expo Proceedings, Reno, USA.   [Google Scholar]
  10. Makhtar M, Harun NA, Abd Aziz A, Zakaria ZA, Abdullah FS, and Jusoh JA (2016). An association rule mining approach in predicting flood areas. In the International Conference on Soft Computing and Data Mining, Springer, Bandung, Indonesia: 437-446. https://doi.org/10.1007/978-3-319-51281-5_44   [Google Scholar]
  11. Murshed MS, Am Seo Y, and Park JS (2014). LH-moment estimation of a four parameter kappa distribution with hydrologic applications. Stochastic Environmental Research and Risk Assessment, 28(2): 253-262. https://doi.org/10.1007/s00477-013-0746-6   [Google Scholar]
  12. Murshed MS, Seo YA, Park JS, and Lee Y (2018). Use of beta-P distribution for modeling hydrologic events. Communications for Statistical Applications and Methods, 25(1): 15-27. https://doi.org/10.29220/CSAM.2018.25.1.015   [Google Scholar]
  13. Park JS and Kim TY (2007). Fisher information matrix for a four-parameter kappa distribution. Statistics and Probability Letters, 77(13): 1459-1466. https://doi.org/10.1016/j.spl.2007.03.002   [Google Scholar]
  14. Park JS, Seo SC, and Kim TY (2009). A kappa distribution with a hydrological application. Stochastic Environmental Research and Risk Assessment, 23(5): 579-586. https://doi.org/10.1007/s00477-008-0243-5   [Google Scholar]
  15. Rao AR and Hamed KH (2000) Flood frequency analysis. CRC Press, Boca Raton, USA.   [Google Scholar]
  16. Samantaray S and Sahoo A (2021). Estimation of flood frequency using statistical method: Mahanadi River basin, India. H2Open Journal, 3(1): 189-207. https://doi.org/10.2166/h2oj.2020.004   [Google Scholar]
  17. Sharafi M, Rezaei A, and Tavangar F (2021). Comparing estimation methods for the three-parameter kappa distribution with application to precipitation data. Hydrological Sciences Journal, 66(6): 991-1003. https://doi.org/10.1080/02626667.2021.1903010   [Google Scholar]
  18. Wang QJ (1997). LH moments for statistical analysis of extreme events. Water Resources Research, 33(12): 2841-2848. https://doi.org/10.1029/97WR02134   [Google Scholar]
  19. Zakaria ZA, Suleiman JMA, and Mohamad M (2018). Rainfall frequency analysis using LH-moments approach: A case of Kemaman Station, Malaysia. International Journal of Engineering Technology, 7(2): 107-110. https://doi.org/10.14419/ijet.v7i2.15.11363   [Google Scholar]
  20. Zhou CR, Chen YF, Huang Q, and Gu SH (2017). Higher moments method for generalized Pareto distribution in flood frequency analysis. In the IOP Conference Series: Earth and Environmental Science, IOP Publishing, Qingdao, China, 82: 012031. https://doi.org/10.1088/1755-1315/82/1/012031   [Google Scholar]