A ratio-type weighted geometric distribution for modelling overdispersed count data
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, repres...
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2025
|
| Online Access: | http://journalarticle.ukm.my/25078/ http://journalarticle.ukm.my/25078/1/SSB%2025.pdf |
| _version_ | 1848816263007043584 |
|---|---|
| author | Shin, Zhu Sim Bakouch, Hassan S. Razik Ridzuan Mohd Tajuddin, Ulya Abdul Rahim, |
| author_facet | Shin, Zhu Sim Bakouch, Hassan S. Razik Ridzuan Mohd Tajuddin, Ulya Abdul Rahim, |
| author_sort | Shin, Zhu Sim |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | 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 w(x) =(x +1) / (x + 2). 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. |
| first_indexed | 2025-11-15T01:03:05Z |
| format | Article |
| id | oai:generic.eprints.org:25078 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T01:03:05Z |
| publishDate | 2025 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:250782025-04-09T03:29:55Z http://journalarticle.ukm.my/25078/ A ratio-type weighted geometric distribution for modelling overdispersed count data Shin, Zhu Sim Bakouch, Hassan S. Razik Ridzuan Mohd Tajuddin, Ulya Abdul Rahim, 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 w(x) =(x +1) / (x + 2). 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. Penerbit Universiti Kebangsaan Malaysia 2025 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/25078/1/SSB%2025.pdf Shin, Zhu Sim and Bakouch, Hassan S. and Razik Ridzuan Mohd Tajuddin, and Ulya Abdul Rahim, (2025) A ratio-type weighted geometric distribution for modelling overdispersed count data. Sains Malaysiana, 54 (1). pp. 313-323. ISSN 0126-6039 https://www.ukm.my/jsm/english_journals/vol54num1_2025/contentsVol54num1_2025.html |
| spellingShingle | Shin, Zhu Sim Bakouch, Hassan S. Razik Ridzuan Mohd Tajuddin, Ulya Abdul Rahim, A ratio-type weighted geometric distribution for modelling overdispersed count data |
| title | A ratio-type weighted geometric distribution for modelling overdispersed count data |
| title_full | A ratio-type weighted geometric distribution for modelling overdispersed count data |
| title_fullStr | A ratio-type weighted geometric distribution for modelling overdispersed count data |
| title_full_unstemmed | A ratio-type weighted geometric distribution for modelling overdispersed count data |
| title_short | A ratio-type weighted geometric distribution for modelling overdispersed count data |
| title_sort | ratio-type weighted geometric distribution for modelling overdispersed count data |
| url | http://journalarticle.ukm.my/25078/ http://journalarticle.ukm.my/25078/ http://journalarticle.ukm.my/25078/1/SSB%2025.pdf |