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PROSES SEMI_MARKOV DAN APLIKASINYA DALAM ASURANSI JIWA Fevi Novkaniza
STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 3, No 1 (2003)
Publisher : Program Studi Statistika Unisba

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jstat.v3i1.527

Proses semi-Markov merupakan pengembangan dari Proses Stokastik Markov. Dalam proses semi-Markov, sifatMarkov tidak lagi dipenuhi, artinya untuk memprediksi state yang akan datang tidak hanya berdasarkan state sekarang, tetapijuga lamanya waktu berada di state ini sebelum pindah ke state yang kan datang. Secara umum dalam asuransi jiwa diasumsikanbahwa “rate of mortality” tidak hanya tergantung dari usia tetapi juga tergantung dari durasi waktu atau lamanya nasabahdiasuransikan. Ketergantungan terhadap durasi waktu ini akan dimodelkan dengan model semi-markov.

Pemodelan Harga Saham Berdasarkan Generalized Linear Model untuk Kejadian Multivariat Fevi Novkaniza; Jonathan Anthony; Rahmat Al Kafi
Limits: Journal of Mathematics and Its Applications Vol 20, No 3 (2023)
Publisher : Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/limits.v20i3.19079

Kejadian multivariat adalah kejadian-kejadian yang memiliki tidak hanya satu peristiwa yang memengaruhi, tetapi bisa lebih banyak peristiwa yang memberi dampak pada peristiwa utamanya. Dampak yang dihasilkan dari suatu kejadian dapat berupa apa saja dan bisa diprediksi. Hal ini menyebabkan perlunya dibentuk sebuah model untuk memprediksi dampak dari sebuah kejadian sehingga dapat diambil keputusan penting berdasarkan kejadian tersebut. Saham merupakan salah satu contoh yang dapat direpresentasikan sebagai kejadian multivariat, seperti harga saham saat penutupan atau closing price, harga maksimal penutupan saham pada periode tertentu, dan durasi waktu (bulanan). Harga penutupan saham dan harga maksimal penutupan saham pada periode tertentu merupakan variabel acak kontinu yang masing-masing diasumsikan berdistribusi eksponensial dan truncated logistic. Durasi waktu (bulanan) merupakan variabel acak diskrit yang diasumsikan berdistribusi geometrik. Untuk mengakomodir kejadian multivariat yang melibatkan ketiga variabel acak tersebut digunakan distribusi trivariat yaitu, distribusi TETLG (Trivariate distribution with Exponential, Truncated Logistic, and Geometric marginals). Selanjutnya, untuk mengetahui pola hubungan antara ketiga variabel acak sebagai vektor respon dengan tiga kovariat yaitu, tingkat pengangguran, tingkat inflasi, dan tingkat obligasi 10 tahun, dikonstruksi sebuah Generalized Linear Model (GLM) untuk kejadian multivariat. Estimasi parameter model GLM kejadian multivariat, dilakukan menggunakan metode Maximum Likelihood. Sebagai implementasi pemodelan harga saham menggunakan GLM kejadian multivariat, diterapkan pada data harga penutupan saham dari Yahoo! Finance untuk periode 2 Januari 1958 hingga 17 April 2020. Berdasarkan uji likelihood ratio, diperoleh hasil bahwa hanya tingkat inflasi dan tingkat pengangguran yang memiliki pengaruh signifikan terhadap pemodelan harga saham.

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

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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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.

Modelling the Number of Stunting Under-Five Children in East Nusa Tenggara Using Negative Binomial Regression Honesty Citra Mar’ati; Dian Lestari; Fevi Novkaniza
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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Malnutrition is an imbalance in a person's energy intake or nutrition. Stunting is one of the nutritional problems in toddlers, where stunting is a condition of growth failure in children under five caused by malnutrition. In Indonesia, East Nusa Tenggara Province has the highest number of toddlers with stunting cases. Therefore, efforts are needed to reduce the number of stunting, especially in East Nusa Tenggara. Several factors are thought to be closely related to the high number of stunting in toddlers. This study aims to find factors that can significantly explain stunting in East Nusa Tenggara to help accelerate the decrease in the number of stunting. This study will explore stunting data from the Ministry of Home Affairs in 2021 for data on East Nusa Tenggara and the Central Statistics Agency of East Nusa Tenggara Province. The appropriate modelling for the number of stunting is the Poisson regression model because the number of stunting is in the form of count data. The proper modelling for stunting cases in toddlers is the Poisson regression model because stunting cases in toddlers are in the form of count data. There is an overdispersion problem to overcome overdispersion in the Poisson regression model; a more suitable Poisson regression model is used as an alternative model. Furthermore, the Maximum Likelihood Estimation (MLE) method estimates the model's parameters. The results showed that the complete immunization variable, pregnant women get nutritional counselling variable, the variable low birth weight babies and the variable of families with beneficiary status had a significant effect on the number of stunting in East Nusa Tenggara.

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

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.

Bayesian Spatial Quantile Regression for Earthquake Risk Assessment and Insurance Pricing in Indonesia Novkaniza, Fevi
JTAM (Jurnal Teori dan Aplikasi Matematika) Vol 9, No 4 (2025): October
Publisher : Universitas Muhammadiyah Mataram

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31764/jtam.v9i4.32415

Indonesia’s geographical location along the Pacific Ring of Fire makes it one of the most seismically active countries in the world, with earthquakes causing recurrent and significant economic losses. To address the need for more accurate and regionally sensitive insurance pricing, this study develops a Bayesian spatial quantile regression model that estimates the 90th percentile of earthquake-induced economic losses. Unlike conventional models that focus on mean losses, this approach captures the upper tail of the loss distribution, which is essential for designing risk financing instruments that can withstand catastrophic events. The model incorporates two main predictors: earthquake magnitude (on the Richter scale) and a provincial risk exposure index constructed from population and GDP per capita. Spatial effects are modelled using a Gaussian kernel with multiple bandwidths. Based on Leave-One-Out Cross-Validation, a bandwidth of 500 kilometers yields the best model performance, effectively capturing regional dependence in earthquake loss data. Historical data from 1930 to 2024 are used to estimate parameters via Markov Chain Monte Carlo sampling with the No-U-Turn Sampler. Results indicate that both earthquake magnitude and socioeconomic exposure are significant drivers of high-end losses. For instance, the model estimates that West Sumatra and Yogyakarta could experience annual benefit payouts exceeding USD 300,000 in high-severity scenarios. Earthquake insurance premiums are then derived using the expected payout values and a 10% premium loading factor. Premium estimates range from USD 0 to over USD 50,000 across provinces, with 20 out of 34 provinces requiring positive premiums. This study contributes a novel modelling framework that integrates quantile regression, spatial weighting, and exposure-based risk assessment. The results provide a data-driven basis for setting premiums and allocating disaster risk financing more equitably across regions. Limitations include reliance on proxy variables for exposure and the exclusion of building-level vulnerability data, which may affect precision in highly localized assessments.

Pemodelan Harga Saham Berdasarkan Generalized Linear Model untuk Kejadian Multivariat Fevi Novkaniza; Jonathan Anthony; Rahmat Al Kafi
Limits: Journal of Mathematics and Its Applications Vol. 20 No. 3 (2023): Limits: Journal of Mathematics and Its Applications Volume 20 Nomor 3 Edisi No
Publisher : Pusat Publikasi Ilmiah LPPM Institut Teknologi Sepuluh Nopember

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

Kejadian multivariat adalah kejadian-kejadian yang memiliki tidak hanya satu peristiwa yang memengaruhi, tetapi bisa lebih banyak peristiwa yang memberi dampak pada peristiwa utamanya. Dampak yang dihasilkan dari suatu kejadian dapat berupa apa saja dan bisa diprediksi. Hal ini menyebabkan perlunya dibentuk sebuah model untuk memprediksi dampak dari sebuah kejadian sehingga dapat diambil keputusan penting berdasarkan kejadian tersebut. Saham merupakan salah satu contoh yang dapat direpresentasikan sebagai kejadian multivariat, seperti harga saham saat penutupan atau closing price, harga maksimal penutupan saham pada periode tertentu, dan durasi waktu (bulanan). Harga penutupan saham dan harga maksimal penutupan saham pada periode tertentu merupakan variabel acak kontinu yang masing-masing diasumsikan berdistribusi eksponensial dan truncated logistic. Durasi waktu (bulanan) merupakan variabel acak diskrit yang diasumsikan berdistribusi geometrik. Untuk mengakomodir kejadian multivariat yang melibatkan ketiga variabel acak tersebut digunakan distribusi trivariat yaitu, distribusi TETLG (Trivariate distribution with Exponential, Truncated Logistic, and Geometric marginals). Selanjutnya, untuk mengetahui pola hubungan antara ketiga variabel acak sebagai vektor respon dengan tiga kovariat yaitu, tingkat pengangguran, tingkat inflasi, dan tingkat obligasi 10 tahun, dikonstruksi sebuah Generalized Linear Model (GLM) untuk kejadian multivariat. Estimasi parameter model GLM kejadian multivariat, dilakukan menggunakan metode Maximum Likelihood. Sebagai implementasi pemodelan harga saham menggunakan GLM kejadian multivariat, diterapkan pada data harga penutupan saham dari Yahoo! Finance untuk periode 2 Januari 1958 hingga 17 April 2020. Berdasarkan uji likelihood ratio, diperoleh hasil bahwa hanya tingkat inflasi dan tingkat pengangguran yang memiliki pengaruh signifikan terhadap pemodelan harga saham.

Accuracy of the Jian-Yang-Jiang-Liu-Liu Spectral Conjugate Gradient Method in Estimating Extended Exponential Weibull Parameters Tjayadi, Steven; Malik, Maulana; Novkaniza, Fevi
International Journal of Mathematics, Statistics, and Computing Vol. 3 No. 4 (2025): International Journal of Mathematics, Statistics, and Computing
Publisher : Communication In Research And Publications

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.46336/ijmsc.v3i4.244

Life is filled with uncertainty and risk. The analysis of lifetime is needed to be a tool that can manage uncertainty. Lifetime is defined as data that contains the time until the occurrence of an event. Based on its definition, lifetime data is like Hazard rate data or mortality data because mortality data can be defined as data that contains the probability of an object surviving until that moment per unit time interval. The analysis of mortality data aims to model the distribution of time to event and/or the determinants of time to event. One of the distribution models that can be used to analyze mortality data is Weibull distribution. However, the Weibull distribution is not very suitable for modeling the more complex versions of data. Therefore, an extension of the Weibull distribution that is more flexible in modeling data is used, namely the Extended Exponential Weibull (ExEW) distribution. The ExEW distribution has four parameters whose estimation can be calculated using the maximum likelihood estimation (MLE) method. However, parameters estimated with MLE are often too difficult to calculate analytically, hence the use of optimization methods. One of the optimization methods that can be used to determine the estimated parameters of the ExEW distribution is the conjugate gradient method. To date, many conjugate gradient methods have been developed, including the Liu-Feng-Zou (LFZ) spectral conjugate gradient method and the Jian-Yang-Jiang-Liu-Liu (JYJLL) spectral conjugate gradient method. Previous research suggests that the JYJLL spectral conjugate gradient method has more efficient computational performance than the LFZ spectral conjugate gradient method. Through data simulation, this study provides results that the JYJLL spectral conjugate gradient conjugate method has better accuracy than the LFZ spectral conjugate gradient method in parameter estimation of the ExEW distribution. In addition, the ExEW distribution is the most suitable distribution in modeling various forms of Hazard rate data compared to the Weibull and exponential distributions.

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