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All Journal JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Ilmiah Matematika
Kafi, Rahmat Al
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Mathematics

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A Posteriori Premium Rate Calculation using Poisson-Gamma Hierarchical Generalized Linear Model for Vehicle Insurance Novkaniza, Fevi; Putri, Irene Devina; Kafi, Rahmat Al; Devila, Sindy
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 1 (2025): January
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i1.27837

Abstract

This study develops and applies the Poisson-Gamma Hierarchical Generalized Linear Model (PGHGLM) to address the challenge of determining accurate and fair premium rates in vehicle insurance. The PGHGLM models a mixture distribution for the response variable, influenced by random effects, and employs a logarithmic link function. Parameter estimation is conducted using the maximum likelihood method. However, since analytical estimation is not feasible, the numerical conjugate gradient method, specifically the Fletcher-Reeves algorithm, is utilized. The implementation of the PGHGLM uses the longitudinal Claimslong dataset, incorporating driver age as a covariate. The main contribution of this research lies in integrating a priori risk classification with a posteriori adjustment based on longitudinal claim frequency data. For datasets without covariates, trend parameters are incorporated into the model. For datasets with covariates, such as driver age, the average claim frequency is computed for each age category. Results show that posteriori premium rates increase with rising claim frequency from the previous year, with higher claim frequencies leading to larger rate adjustments in the subsequent year. Through the PGHGLM, a posteriori premium rate estimates are obtained for each age group of vehicle insurance policyholders. This study demonstrates the practical application of the PGHGLM in calculating precise premium rates. By analyzing a longitudinal vehicle insurance dataset, the model generates annual a posteriori premium rates tailored to age groups. These findings underscore the PGHGLM’s robust methodological framework and its potential to enhance premium fairness, enable risk-adjusted pricing, and better tailor insurance products to diverse policyholder profiles. 
Analysis of diabetes mellitus gene expression data using two-phase biclustering method Kafi, Rahmat Al; Bustamam, Alhadi; Mangunwardoyo, Wibowo
Jurnal Ilmiah Matematika Vol 8, No 2 (2021)
Publisher : Universitas Ahmad Dahlan

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.26555/konvergensi.v0i0.22111

Abstract

The purpose of this research is to find bicluster from Type 2 Diabetes Mellitus genes expression data which samples are obese and lean people using two-phase biclustering. The first step is to use Singular Value Decomposition to decompose matrix gene expression data into gene and condition based matrices. The second step is to use K-means to cluster gene and condition based matrices, forming several clusters from each matrix. Furthermore, the silhouette method is applied to determine the number of optimum clusters and measure the accuracy of grouping results. Based on the experimental results, Type 2 Diabetes Mellitus dataset with 668 selected genes produced optimal biclusters, with six biclusters. The obtained biclusters consist of 2 clusters on the gene-based matrix and 3 clusters on the sample-based matrix with silhouette values, respectively, are 0.7361615 and 0.7050163.
Co-Authors Bustamam, Alhadi Devila, Sindy fevi novkaniza Putri, Irene Devina WIBOWO MANGUNWARDOYO