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All Journal LOGIK@ BAREKENG: Jurnal Ilmu Matematika dan Terapan Jurnal Statistika dan Aplikasinya PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON DATA SCIENCE AND OFFICIAL STATISTICS
Fithriani, Ida
Departemen Matematika, Fakultas Matematika Dan Ilmu Pengetahuan Alam, Universitas Indonesia, Depok 16424, Indonesia.
Agriculture, Biological Sciences & Forestry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation Other

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PEMBENTUKAN DISTRIBUSI TRANSMUTED EXPONENTIATED EXPONENTIAL MENGGUNAKAN METODE QUADRATIC RANK TRANSMUTATION MAP (QRTM) Siti Nurohmah; Ida Fithriani; Ridho Okta Pawarestu
LOGIK@ Vol 6, No 2 (2016)
Publisher : Universitas Islam Negeri Syarif Hidayatullah Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (511.71 KB)

Abstract

Distribusi  Transmuted Exponentiated Exponential  merupakan generalisasi dari distribusi  Exponentiated Exponential  yang dibentuk dengan menggunakan metode  Quadratic Rank TransmutatioMaps  (QRTM).  Distribusi Transmuted Exponentiated Exponential  merupakan salah satu distribusi kontinu yang mampu memodelkan data dengan hazard rate naik, turun, bathtub, dan non-monoton. Pada penulisan ini akan dibahas  mengenai  proses pembentukan distribusi Transmuted Exponentiated Exponential  serta   karakteristik-karakteristik dari distribusi yang meliputi fungsi kepadatan probabilitas, fungsi distribusi, dan hazard rate.
Model Kredibilitas Bühlmann dengan Risiko Bersama Muhammad Imanudin Saputra; Siti Nurrohmah; Ida Fithriani
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.06107

Abstract

Penyedia jasa asuransi dalam praktiknya menanggung risiko pemegang polis dengan membayarkan klaim yang diajukan oleh pemegang polis. Sebagai gantinya, pemegang polis perlu membayarkan premi kepada penyedia jasa asuransi. Oleh karena itu diperlukan prediksi besar klaim yang akan diajukan sehingga dapat ditentukan juga besar premi yang perlu dibayarkan oleh pemegang polis. Salah satu cara untuk memprediksi besar klaim adalah dengan menggunakan teori kredibilitas. Teori kredibilitas memungkinkan penyedia jasa asuransi untuk menggunakan informasi dari pengalaman klaim seorang individu dengan informasi lainnya berupa manual rate dalam memprediksi besar klaim di masa yang akan datang. Salah satu model yang dikembangkan dalam teori kredibilitas adalah model kredibilitas Buhlmann. Pada model kredibilitas Buhlmann, diasumsikan risiko antara individu saling independen. Namun dalam beberapa kasus asumsi tersebut tidak terpenuhi. Selain itu, model kredibilitas Buhlmann menggunakan fungsi kerugian berupa squared error loss function untuk mendapatkan estimator kredibilitas model. Pada penelitian ini dijelaskan pembentukan estimator kredibilitas model kredibilitas Buhlmann yang memperhitungkan dependensi risiko antara individunya yang dijelaskan oleh suatu parameter risiko bersama dengan menggunakan proyeksi orthogonal dan fungsi kerugian berupa balanced loss function (BLF). Dengan menggunakan data yang memenuhi asumsi model, dapat diperoleh besar presisi dan goodness of fit dari estimasi klaim yang berbeda-beda dengan mengatur bobot pada BLF.
Metode Bayesian Chain Ladder untuk Memprediksi Cadangan Klaim Nadya Arifani; Siti Nurrohmah; Ida Fithriani
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.06111

Abstract

Perusahaan asuransi perlu mempersiapkan sejumlah uang yang disebut dengan cadangan klaim untuk membayar klaim yang akan terjadi di masa depan. Salah satu metode yang sering digunakan untuk memprediksi cadangan klaim adalah metode Chain Ladder. Metode ini memprediksi cadangan klaim menggunakan estimasi development factor yang menyatakan perkembangan besar klaim pada setiap periode penundaan pembayaran klaim. Namun, metode Chain Ladder hanya murni menggunakan kumpulan data pembayaran klaim-klaim masa lalu. Padahal, tidak menutup kemungkinan ada informasi penting lainnya yang dapat digunakan untuk memprediksi cadangan klaim. Salah satu informasi tersebut adalah informasi masa lalu yang diperoleh dari pengalaman serupa ataupun dari sesuatu yang dipercaya oleh para ahli. Wüthrich and Merz (2015) mengembangkan metode Bayesian Chain Ladder yang menerapkan teori Bayesian untuk menambahkan informasi masa lalu ke dalam metode Chain Ladder. Untuk memprediksi cadangan klaim, metode Bayesian Chain Ladder menggunakan Bayesian development factor dengan mengonstruksikan distribusi pada informasi prior (informasi masa lalu) dan distribusi dari data yang diamati. Distribusi yang digunakan adalah distribusi Gamma sebagai distribusi prior dan distribusi data. Secara umum, makalah ini membahas mengenai penerapan teori Bayesian pada metode Chain Ladder serta ditampilkan juga simulasi numerik menggunakan data perusahaan asuransi umum di Amerika Serikat. Didapatkan hasil bahwa metode Bayesian Chain Ladder memberikan prediksi cadangan klaim yang bergantung pada bobot kepercayaan dalam mempertimbangkan informasi masa lalu yang digunakan dalam model. Bobot kepercayaan yang berbeda akan selalu menghasilkan prediksi cadangan klaim yang berbeda. Perbedaan bobot kepercayaan yang dipilih tergantung dari pendapat para ahli, sehingga prediksi cadangan klaim dengan menggunakan metode Bayesian Chain Ladder bersifat subjektif.
hyper-Poisson Model for Overdispersed and Underdispersed Count Data Venda Damianus Situmorang; Siti Nurrohmah; Ida Fithriani
Proceedings of The International Conference on Data Science and Official Statistics Vol. 2023 No. 1 (2023): Proceedings of 2023 International Conference on Data Science and Official St
Publisher : Politeknik Statistika STIS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34123/icdsos.v2023i1.344

Abstract

The Poisson model is commonly used for modelling count data. However, it has a limitation, namely the equality between the mean and variance (equidispersion) of the data to be modeled. Unfortunately, overdispersion (variance greater than the mean) and underdispersion (variance smaller than the mean) are more often to be found in real cases. Therefore, different models need to be used to handle data with these cases. The hyper-Poisson model is one model that can be used to handle overdispersion or underdispersion cases flexibly. This paper describes the hyper-Poisson model and its application on overdispersed and underdispersed count data.
Vine Copula Model: Application to Chemical Elements in Water Samples Salsabila Zahra Aminullah; Mila Novita; Ida Fithriani
Proceedings of The International Conference on Data Science and Official Statistics Vol. 2023 No. 1 (2023): Proceedings of 2023 International Conference on Data Science and Official St
Publisher : Politeknik Statistika STIS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34123/icdsos.v2023i1.346

Abstract

Copula can link the bivariate distribution function with marginal distribution functions without requiring specific information about the interdependence among random variables. There are several types of copulas, such as elliptical copulas, Archimedean copulas, and extreme value copulas. However, in multivariate modeling, each type of copula has limitations in modeling complex dependence structures in terms of symmetry and tail dependence properties. The class of vine copulas overcomes these limitations by constructing multivariate models using bivariate copulas in a tree-like structure. The bivariate copulas used in this study include the Clayton, Gumbel, Frank, Gaussian, and Student's t copula families. This study discusses the construction of vine copula models, parameter estimation, and their applications. The construction of vine copulas is done through the decomposition of conditional probability density functions and substituting bivariate copula density functions into the decomposition results. The data used in the study is the logarithm of the concentration of chemical elements in water samples in Colorado. The parameter estimation method used is pseudo-maximum likelihood with sequential estimation. Model selection is then performed using the Akaike information criterion (AIC) to determine the most suitable model. The results indicate that Caesium and Titanium have a dependency relationship with Scandium. Moreover, Scandium and Titanium exhibit the strongest dependence compared to other variable pairs.
Formulation of Kumaraswamy Generalized Inverse Lomax Distribution Andrew Bony Nabasar Manurung; Siti Nurrohmah; Ida Fithriani
Proceedings of The International Conference on Data Science and Official Statistics Vol. 2023 No. 1 (2023): Proceedings of 2023 International Conference on Data Science and Official St
Publisher : Politeknik Statistika STIS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.34123/icdsos.v2023i1.416

Abstract

Lifetime data is a type of data that consists of a waiting time until an event occurs and modelled by numerous distributions. One of its characteristics that is interesting to be studied is the hazard function due to the flexibility that it has compared to other characteristics of distribution. Inverse Lomax (IL) distribution is one of the distributions considered to have advantages in modelling hazard shape and extended in several ways to address the problem of non-monotone hazard which is often encountered in real life data. However, it needs to be extended to another family of distribution to increase its modelling potential and Kumaraswamy Generalized (KG) family of distribution is used as it adds two more parameters to the distribution. The newly developed distribution is called the Kumaraswamy Generalized Inverse Lomax (KGIL) distribution. The main characteristics of KGIL distribution will be derived, such as cumulative distribution function (cdf), probability density function (pdf), hazard function, and survival function. Maximum likelihood method will also be used to estimate the parameters. The application of the new model is based on head-and-neck cancer lifetime data set. The modelling results show that the KGIL distribution is the best to capture important details of the data set considered
MODELING THE BENEFITS OF A MARRIAGE REVERSE ANNUITY CONTRACT WITH DEPENDENCY ASSUMPTIONS USING ARCHIMEDEAN COPULA Lundy, Arnhilda Aspasia; Novita, Mila; Fithriani, Ida
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 18 No 4 (2024): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol18iss4pp2137-2152

Abstract

Social security benefits may not be enough for retirement. Equity release products like marriage reverse annuities can boost retirement income for older couples. Marriage reverse annuity’s contract convert all or part of the real estate value of elderly spouses while they are living (joint life status) or after one partner dies (last survivor status). Since husband and wife face the same death risk, the chance of death between spouses is believed to be dependent for realism. Thus, copula models the future dependency model of a husband and wife. Sklar's theorem states that copulas link bivariate distribution and marginal cumulative functions. One of the most common copulas is Archimedean copula. Clayton, Gumbel, and Frank are Archimedean copula that will be used in this investigation. The Indonesian Mortality Table IV data is used to obtain the marginal distribution of the male and female which will then be used to construct copulas (Clayton, Gumbel, and Frank) that combine two marginal distributions into a joint distribution. The marginal distribution of Indonesian Mortality Table IV is uncertain, hence Canonical Maximum Likelihood parameter estimation is utilized to estimate the parameter of copulas. Multiple-state models depict the marriage reverse annuity model for joint life and last survivor status. The probability structure is based on Sklar's theorem and copula survival function. The contract benefits calculation utilizing copulas (Clayton, Gumbel, and Frank) shows that joint life status benefits are higher than last survivor status. Joint life status uses the dependence assumption with Frank's copula to calculate the smallest annual benefit value of a marriage reverse annuity contract, while last survivor status uses the independence assumption (without copula).
Co-Authors Andrew Bony Nabasar Manurung Lundy, Arnhilda Aspasia Mila Novita Muhammad Imanudin Saputra Nadya Arifani Novita, Mila Ridho Okta Pawarestu Salsabila Zahra Aminullah Siti Nurohmah Siti Nurrohmah Siti Nurrohmah Siti Nurrohmah Siti Nurrohmah Venda Damianus Situmorang