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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan JTAM (Jurnal Teori dan Aplikasi Matematika) Jurnal Statistika dan Aplikasinya Asian Journal of Management, Entrepreneurship and Social Science
Sindy Devila
Department Of Mathematics , Faculty Of Mathematics And Natural Science, Universitas Indonesia
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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Model Kredibilitas Bühlmann Berdasarkan Data Terpancung Vicko Regenio Widodo; Siti Nurrohmah; Sindy Devila
Jurnal Statistika dan Aplikasinya Vol 6 No 1 (2022): Jurnal Statistika dan Aplikasinya
Publisher : Program Studi Statistika FMIPA UNJ

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.21009/JSA.06110

Abstract

Setiap orang pasti menghadapi suatu risiko di masa depan. Seseorang dapat mengurangi besarnya kerugian akibat risiko tertentu dengan membeli asuransi. Asuransi mewajibkan seorang pemegang polis membayar premi secara periodik. Salah satu model yang dapat digunakan dalam penentuan premi adalah model kredibilitas Bühlmann. Paper ini membahas model kredibilitas yang didasarkan pada model kredibilitas Bühlmann tetapi melibatkan pemancungan data kerugian asli di kuantil ke-p dan kuantil ke-q. Model ini menggunakan trimmed mean untuk memprediksi besar kerugian di periode berikutnya yaitu ekspektasi kerugian untuk suatu risiko tertentu dengan syarat kerugian tersebut sudah terpancung. Model kredibilitas ini memiliki beberapa kelebihan, salah satunya yaitu premi kredibilitas yang didapat tidak terlalu terpengaruh terhadap outlier. Pembahasan pada paper ini berfokus pada penjabaran hasil teoritis untuk membangun model kredibilitas berdasarkan data terpancung dan pengestimasian parameter dengan menggunakan metode non-parametrik pada model kredibilitas berdasarkan data terpancung. Model kredibilitas berdasarkan data terpancung ini diimplementasikan pada suatu sampel data kerugian terurut. Sampel ini merupakan data kerugian asli untuk 30 individu dengan periode 20 tahun yang telah diurutkan dari yang terkecil hingga terbesar. Analisis dilakukan terhadap perhitungan parameter model di berbagai kasus. Selain itu, dibahas perbandingan sensitivitas premi pada model kredibilitas berdasarkan data terpancung dan model kredibilitas Bühlmann jika terdapat outlier. Berdasarkan hasil penelitian, model kredibilitas berdasarkan data terpancung dapat menentukan risk loading dan tidak terlalu terpengaruh terhadap outlier dibandingkan dengan model kredibilitas Bühlmann.
Modeling the Number of Acute Hepatitis Sufferers in DKI Jakarta using Negative Binomial Regression Wildan Alrasyid; Dian Lestari; Fevi Novkaniza; Arman Haqqi; Sindy Devila
Asian Journal of Management, Entrepreneurship and Social Science Vol. 3 No. 02 (2023): May, Asian Journal of Management, Entrepreneurship and Social Science
Publisher : Cita Konsultindo Research Center

Show Abstract | Download Original | Original Source | Check in Google Scholar

Abstract

Hepatitis is an inflammation of the liver due to viral infections. All viral hepatitis can cause acute hepatitis. Hepatitis is an infectious disease that is a major health problem in the community because of its relatively easy transmission. DKI Jakarta is the province in Indonesia with the highest cases of acute hepatitis. Therefore, efforts need to be made to reduce the number of acute hepatitis sufferers, especially in DKI Jakarta. Several factors are thought to be closely related to the high number of acute hepatitis cases. The purpose of this study is to find factors that can significantly explain the case of hepatitis disease in DKI Jakarta so that measures can be taken to prevent the emergence of acute hepatitis cases in the community. The data in this study was obtained from the DKI Jakarta health office in 2021. The appropriate modeling for the number of people with acute hepatitis is a poisson regression model because the number of people with acute hepatitis is a count of data. In overcoming cases of overdispersion in poisson regression models, a more suitable Negative Binomial regression model is used as an alternative. In this study, the estimation of model parameters was carried out using the Maximum Likelihood Estimation (MLE) method. The results of the analysis found 3 variables that significantly explain the number of acute hepatitis sufferers in DKI Jakarta, namely the number of places of management that meet health standards, the number of health workers, and the number of HIV sufferers.
Modeling The Number of Toddler Pneumonia Sufferers in DKI Jakarta using Negative Binomial Regression Lucky Simarda; Dian Lestari; Fevi Novkaniza; Arman Haqqi; Sindy Devila
Asian Journal of Management, Entrepreneurship and Social Science Vol. 4 No. 01 (2024): Pebruary, Asian Journal of Management Entrepreneurship and Social Science ( AJ
Publisher : Cita Konsultindo Research Center

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Abstract

Acute lung tissue infection caused by various microorganisms, including fungi, viruses, and bacteria, is known as pneumonia. Pneumonia is the highest cause of child death worldwide. In Indonesia, pneumonia remains the leading cause of death among toddler (12-59 months old). By 2021, the national coverage of pneumonias among toddler was 34.8%, and the provinces with the highest coverage for toddler pneumonia were DKI Jakarta (53.0%), Banten (46.0%), and West Papua (45,7%). To find out the pattern of the relationship between the number of young people with pneumonia and the variables that affect it, a custom mathematical model is needed. The number of cases of toddler pneumonia in DKI Jakarta is a data count distributed by Poisson. Poisson regression is perfectly suitable for analyzing data that qualifies equidispersion. However, on the data, the number of toddler pneumonia cases in DKI Jakarta does not meet the equidispersion condition because the variance value is greater than the average or is called overdispersion. One of the methods developed to deal with overdispersion is negative binomial regression. The analysis showed that the average case of toddler pneumonia in Jakarta DKI was 454, Duren Sawit district recorded the highest case of 1329 cases and Sawah Besar district recorded the lowest case as 50 cases. The AIC criteria indicate that the Negative Binomial Regression model is a suitable model for modeling the number of cases of toddler pneumonia in Jakarta DKI with the smallest AIC value of 592,57. The best modeling results using the negative binomial regression method show two significant variables, they are the numbers of toddlers given exclusive breastfeeding and the numbers toddlers that were affected by covid-19.
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. 
A NEW ONE-PARAMETER DISTRIBUTION FOR MODELING POSITIVE SKEWNESS DATA: THE GENERIC KRISON DISTRIBUTION Elbert Krison; Siti Nurrohmah; Sindy Devila; Ida Fithriani
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 4 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss4pp2769-2782

Abstract

Inspired by the hyperbolic secant distribution and a specific hyperbolic trigonometric identity, we propose a new continuous distribution with one parameter, called the Generic Krison distribution. We derive its probability density function, survival function, cumulative distribution function, hazard function, quantile function, and mean excess loss function. Closed‑form expressions for the moment generating function are also provided. Statistical measures including the raw moments, mean, variance, standard deviation, median, mode, skewness, kurtosis, coefficient of variation, and index of dispersion are obtained. The distribution exhibits constant moderate positive skewness and a constant coefficient of variation, making it a natural candidate for modeling positively skewed data. The parameter is estimated by the method of maximum likelihood; because the score equation is transcendental, the estimate is obtained numerically. We compare the Generic Krison distribution with the one‑parameter Rayleigh, Lindley, and Bilal distributions across three datasets (income, survival time, mortality rate). The results demonstrate that the Generic Krison distribution performs well on all three datasets, offering a promising new tool for statistical modeling.
Co-Authors Alrasyid, Wildan Arman Haqqi Arman Haqqi Dian Lestari Dian Lestari Elbert Krison fevi novkaniza Fithriani, Ida Kafi, Rahmat Al Lucky Simarda Maulana Malik Putri, Irene Devina Siti Nurrohmah Siti Nurrohmah Vicko Regenio Widodo Wed Giyarti