Sains Malaysiana 54(1)(2025): 313-323

http://doi.org/10.17576/jsm-2025-5401-25

 

A Ratio-Type Weighted Geometric Distribution for Modelling Overdispersed Count Data

(Taburan Geometri Berpemberat Jenis Nisbah untuk Memodelkan Data Bilangan Terlebih Serakan)

 

SHIN ZHU SIM¹, HASSAN S. BAKOUCH^2,3, RAZIK RIDZUAN MOHD TAJUDDIN^4,* & ULYA ABDUL RAHIM⁵

 

¹School of Mathematical Sciences, University of Nottingham Malaysia, 43500 Semenyih, Selangor, Malaysia
²Department of Mathematics, College of Science, Qassim University, Buraydah, Saudi Arabia
³Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
⁴Department of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia
⁵Deanery Office, Faculty of Medicine, Universiti Kebangsaan Malaysia, 43600 UKM Bangi, Selangor, Malaysia

 

Received: 11 June 2024/Accepted: 7 October 2024

 

Abstract

Weighted distributions have always been a popular approach in developing flexible distributions for data modelling. In this paper, we introduce a flexible ratio-type weighted geometric distribution by adopting the geometric distribution as a basic standard distribution and opting for weights, represented as . The proposed distribution is overdispersed and is capable of accommodating data with small mode values such as 0, 1 and 2. The proposed distribution has the following properties – unimodal, log-concave and has increasing failure rates. The moment estimator is obtained, and the resulting estimated parameter is utilized as the initial point in finding the estimators based on the maximum likelihood technique and probability generating function. A probability comparison between the typical geometric distribution and the proposed distribution is discussed as well. A collection of insurance claim datasets is utilized for model fitting, and it was found out that generally, the proposed distribution can adequately fit the datasets as opposed to other contending distributions.

 

Keywords: Discrete distributions; estimation geometric; simulation; weights

 

Abstrak

Taburan berpemberat selalu menjadi pendekatan yang popular dalam mengembangkan taburan fleksibel untuk pemodelan data. Dalam kajian ini, kami memperkenalkan taburan geometrik berpemberat jenis nisbah yang fleksibel dengan mengambil kira taburan geometrik sebagai taburan piawai asas dan memilih berat, yang diwakili sebagai . Taburan yang dicadangkan adalah terlebih serak dan mampu mengendalikan data dengan nilai mod kecil seperti 0, 1 dan 2. Taburan yang dicadangkan mempunyai sifat berikut – unimodal, log-cekung dan mempunyai kadar kegagalan yang meningkat. Penganggar momen diperoleh, dan parameter yang dianggarkan digunakan sebagai titik permulaan dalam mencari penganggar berdasarkan teknik kebolehjadian maksimum dan fungsi penjana kebarangkalian. Perbandingan kebarangkalian antara taburan geometrik biasa dan taburan yang dicadangkan turut dibincangkan. Koleksi set data tuntutan insurans digunakan untuk pemodelan dan didapati bahawa secara umum, taburan yang dicadangkan dapat memadankan set data dengan baik berbanding taburan lain yang dipertimbangkan.

 

Kata kunci: Geometrik; pemberat; penganggaran; simulasi; taburan diskret

 

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*Corresponding author; email: rrmt@ukm.edu.my