Sains Malaysiana 39(4)(2010): 647–653

Penggunaan Gambar Rajah Nisbah LQ-Momen dalam Pemilihan Taburan Terbaik

(Application of LQ-Moment Ratio Diagram in Selecting the Best Distribution)

Ani bin Shabri*

Jabatan Matematik, Fakulti Sains, Universiti Teknologi Malaysia

81310 UTM Skudai Johor, Malaysia

Abdul Aziz Jemain

Pusat Pengajian Sains Matematik, Fakulti Sains dan Teknologi

Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor D.E., Malaysia

Received: 3 July 2009 / Accepted: 21 January 2010

ABSTRAK

Kaedah momen merupakan salah satu teknik termudah dan sering digunakan dalam statistik hidrologi. Bagaimanapun, penganggar momen selalunya memberikan kualiti yang rendah dan tidak sebaik penganggar L-momen terutamanya untuk taburan dengan tiga parameter atau lebih. Pada masa kini, banyak kajian analisis frekuensi serantau dalam hidrologi menggunakan gambar rajah nisbah L-momen untuk memilih taburan yang sesuai bagi data hidrologi dan meteorologi. Kelebihan utama gambar rajah nisbah L-momen adalah pemilihan beberapa taburan yang sesuai boleh dilakukan menggunakan satu graf sahaja. Tujuan utama kertas ini untuk melihat kembali LQ-momen dan untuk membangunkan gambar rajah LQ-momen berdasarkan penganggar median. Menggunakan data aliran banjir dari 73 buah stesen dalam Semenanjung Malaysia, kami meninjau kesesuaian pelbagai model kebarangkalian menggunakan gambar rajah nisbah LQ-momen dan dibandingkan dengan gambar rajah nisbah L-momen. Hasil kajian menunjukkan gambar rajah nisbah LQ-momen secara umumnya memberikan keupayaan yang baik sebagaimana gambar rajah nisbah L-momen dalam memilih taburan frekuensi dan ini membuatkan ianya sesuai untuk dijadikan sebagai pilihan yang menarik untuk digunakan dalam analisis frekuensi banjir.

Kata kunci: Frekuensi serantau; gambar rajah nisbah L-momen; L-momen; LQ-momen; Momen

ABSTRACT

The method of moments has been one of the simplest and conventional parameter estimation techniques used in statistical hydrology. However, moment estimates are usually inferior in quality and generally not as efficient as the L-moment estimates, especially for distribution with three or more parameters. Of late, many regional frequency studies in hydrology use the L-moment ratio diagram to select the most appropriate distribution of hydrologic and meteorological data. An advantage of L-moment ratio diagrams is that one can compare the fit of several distributions using a single graphical instrument. The purpose of this paper is to revisit the LQ moments and to develop the LQ-moments ratio diagrams based on median estimator. Using flood-flow data at 73 stations in Peninsular Malaysia, we explored the suitability of various flood frequency models using LQ-moments ratio diagrams compared with L-moments ratio diagrams. The result shows that the new diagrams perform as well as L-moments ratio diagrams for selecting a suitable frequency distributions and makes it an attractive option in flood frequency analysis.

Keywords: L-moments; Moments, L-moment ratio diagrams; LQ-moments; regional frequency

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*Corresponding author; email: ani@utm.my