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All Journal LOGIK@ Statistika CAUCHY: Jurnal Matematika Murni dan Aplikasi Desimal: Jurnal Matematika BAREKENG: Jurnal Ilmu Matematika dan Terapan M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika InPrime: Indonesian Journal Of Pure And Applied Mathematics Majalah Ilmiah Matematika dan Statistika (MIMS) Jambura Journal of Biomathematics (JJBM) The Indonesian Journal of Computer Science
Nina Fitriyati
Unknown Affiliation
Computer Science & IT Control & Systems Engineering Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Education Electrical & Electronics Engineering Energy Engineering Industrial & Manufacturing Engineering Mathematics Mechanical Engineering Physics Social Sciences Transportation

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The Constant Annual Premium and Benefit Reserve for Four Participants in Joint Life Insurance Nadilia, Nindita; Fitriyati, Nina; Fauziah, Irma
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 2, No 2 (2020)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v2i2.14780

Abstract

AbstractThis research discusses the derivation of formula to calculate the constant annual premiums and the benefit reserves for joint insurance consisting of four people. We combine pure endowment insurance, lifetime insurance, and n-year term insurance. Assumed that the benefits are set at the beginning of the insurance contract, the benefit reserves are calculated using the prospective method, and the premium payment stops if one of those four participants dies. If all participants live until the end of the contract, the benefits are paid at once but if one of the participants dies, the benefits paid at the end of the contract in the form of a lifetime annuity. The formula to calculate the benefit reserves is divided into four cases i.e. the benefit reserves if one of four participants dies, the benefit reserves if two of four participants die, the benefit reserve if three of four participants die, and the benefit reserves if all participants are still alive until the end of the contract. Besides, we also present simulation to calculate the constant annual premium for four participants consist of a father (50 years old), a mother (45 years old), a son (20 years old), and a daughter (15 years old). From the simulation, we conclude that as the length of the insurance contract increases, the premium tends to decrease. The benefit reserve calculation does not have a certain tendency. It generally increases during the insurance period (the premium is still paid) and then decreases thereafter. This is valid for all cases mentioned above.Keywords: n-year term insurance; prospective method; pure endowment insurance. AbstrakPenelitian ini membahas mengenai penurunan rumus untuk menghitung premi tahunan konstan dan cadangan benefit untuk asuransi gabungan yang terdiri dari empat orang. Jenis asuransi yang digunakan adalah kombinasi antara asuransi endowment murni, asuransi seumur hidup dan asuransi berjangka n-tahun. Diasumsikan bahwa benefit ditetapkan di awal kontrak asuransi dan pembayaran premi berhenti jika salah seorang dari keempat peserta meninggal dunia. Jika seluruh peserta hidup sampai dengan akhir kontrak maka benefit dibayarkan secara sekaligus, namun jika salah satu dari peserta telah meninggal dunia maka benefit yang dibayarkan pada akhir tahun kontrak dalam bentuk anuitas seumur hidup. Rumus yang diperoleh untuk menghitung cadangan benefit dibagi menjadi empat kasus yaitu cadangan benefit jika satu orang meninggal dan tiga orang lainnya hidup, cadangan benefit jika dua orang meninggal dan dua orang lainnya hidup, cadangan benefit jika tiga orang meninggal dan satu orang lainnya hidup, dan cadangan benefit jika semua peserta tetap hidup sampai akhir masa kontrak. Pada akhir penelitian, disajikan simulasi perhitungan premi tahunan konstan untuk empat peserta yang terdiri dari ayah (berusia 50 tahun), ibu (45 tahun), anak laki-laki (20 tahun), dan anak perempuan (15 tahun). Dari simulasi diperoleh bahwa semakin lama kontrak asuransi maka premi yang dibayakan cenderung semakin kecil. Perhitungan cadangan benefit tidak memiliki kecenderungan tertentu, namun pada umumnya meningkat selama masa asuransi berlangsung (pembayaran premi masih dilakukan) kemudian menurun setelahnya. Hal ini berlaku untuk seluruh kasus yang telah dibahas pada perhitungan rumus cadangan premi.Kata kunci: asuransi berjangka n-tahun; metode prospektif; asuransi endowment murni.
APLIKASI MODEL GSTAR-I DENGAN PENDEKATAN INVERS MATRIKS AUTOKOVARIANS (IMAk) PADA PRAKIRAAN CURAH HUJAN DI PROVINSI BANTEN Sri Maliska; Nina Fitriyati; . Mahmudi
LOGIK@ Vol 7, No 1 (2017): Vol.7 No.1 Tahun 2017
Publisher : Universitas Islam Negeri Syarif Hidayatullah Jakarta

Show Abstract | Download Original | Original Source | Check in Google Scholar | Full PDF (819.495 KB)

Abstract

Hujan merupakan unsur iklim yang paling penting di Indonesia karena memiliki keragaman yang sangat tinggi baik menurut waktu maupun menurut tempat. Oleh karena itu, kajian mengenai iklim lebih diarahkan pada hujan. Secara umum, curah hujan merupakan data deret waktu yang mempunyai keterkaitan antarlokasi sehingga salah satu model prakiraan yang dapat digunakan adalah model GSTAR-I. Pada penelitian ini, akan dibahas mengenai prakiraan curah hujan menggunakan model GSTAR-I dengan pendekatan Invers Matriks Autokovarians (IMAk). Data yang digunakan adalah data curah hujan di Stasiun Meteorologi Serang, Stasiun Klimatologi Pondok Betung, Stasiun Meteorologi Curug, Stasiun Meteorologi Cengkareng dan Stasiun Geofisika Tangerang. Diasumsikan setiap lokasi memiliki jarak yang sama sehingga digunakan matriks bobot seragam. Hasil identifikasi model menunjukkan bahwa beberapa model GSTAR-I yang mungkin adalah GSTAR-I (1;0), GSTAR-I (2;0), GSTAR-I (3;0), GSTAR-I (1;1) dan GSTAR-I (2;1). Berdasarkan nilai Mean Square Residual (MSR) diperoleh GSTARI (1;0) adalah model prakiraan terbaik.
KLASIFIKASI JENIS PENYAKIT ERYTHEMATO-SQUAMOUS BERDASARKAN CIRI KLINIS DAN HISTOPATOLOGIS MENGGUNAKAN METODE ANALISIS DISKRIMINAN VERTEX Nurmaleni Nurmaleni; Ayu Puji Rahayu; Nina Fitriyati
LOGIK@ Vol 8, No 2 (2018): Vol.8 No.2 Tahun 2018
Publisher : Universitas Islam Negeri Syarif Hidayatullah Jakarta

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Abstract

Penelitian ini membahas mengenai klasifikasi jenis penyakit erythemato-squamous menggunakan metode Vertex Discriminant Analysis (VDA) berdasarkan hasil pemeriksaan klinis dan histopatologis. Digunakan 3 pinalti pada metode VDA yaitu Euclidian, Lasso, dan Ridge dan kesalahan klasifikasi dinilai menggunakan Apparent Rate Error (APER). Data yang digunakan berjumlah 366 terdiri dari 34 buah peubah hasil pemeriksaan klinis dan histopatologis yang berasal dari 6 kelompok penyakit: psoriasis, seboreic dermatits, lichen planus, pityriasis rosea, cronic dermatitis, dan pityriasis rubra pilaris. Hasil menunjukkan bahwa setiap pinalti pada metode VDA membentuk 5 buah fungsi diskriminan untuk membedakan 6 kelompok penyakit. VDA dengan pinalti Euclidian berhasil mengklasifikasikan dengan tepat 104 data dari 110 data training dengan 27 peubah penjelas yang terdiri dari 12 ciri klinis dan 15 ciri hispatologis. VDA dengan pinalti Lasso berhasil mengklasifikasikan dengan tepat 102 data dari 110 data training dengan 25 peubah penjelas yang terdiri dari 11 ciri klinis dan 14 ciri hispatologis. Sedangkan VDA dengan pinalti Ridge berhasil mengklasifikasikan dengan tepat 107 data dari 110 data training dengan 34 peubah penjelas yang terdiri dari 12 ciri klinis dan 22 ciri hispatologis.
APLIKASI KALMAN FILTER DAN ENSEMBLE KALMAN FILTER PADA PENDETEKSIAN GANGGUAN KONDUKSI PANAS PADA KEPING LOGAM BERBENTUK SILINDER Gina Isma Kusuma; Nina Fitriyati
LOGIK@ Vol 7, No 2 (2017): Vol.7 No.2 Tahun 2017
Publisher : Universitas Islam Negeri Syarif Hidayatullah Jakarta

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Abstract

Kebocoran pada keping logam berbentuk silinder dapat menganggu proses perpindahan panas. Oleh karena itu diperlukan suatu metode yang dapat digunakan untuk mendeteksi kebocoran tersebut. Pada penelitian ini, dibahas pengetimasian lokasi kebocoran pada keping logam berbentuk silinder menggunakan metode Kalman filter (KF) dan Ensemble Kalman Filter (EnKF). Persamaan ruang keadaan dibentuk dari diskritisasi persamaan difusi menggunakan metode Beda Hingga Maju dan Beda Hingga Pusat. Data simulasi dibangkitkan dari solusi analitik persamaan difusi. Pada metode EnKF banyaknya ensemble yang digunakan adalah 100, 200, 300, 400, dan 500 buah. Hasil simulasi menunjukkan bahwa kedua metode ini mampu mendeteksi dengan baik lokasi kebocoran pada keping logam berbentuk silinder. Pada metode EnKF, pendeteksian terbaik dihasilkan ketika banyak ensemble 500 karena nilai rata-rata error lebih kecil dibandingkan nilai rata-rata error pada banyak ensemble lainnya. Selain itu, hasil simulasi pun menunjukkan bahwa metode EnKF lebih akurat daripada KF karena rata-rata error dan nilai ratarata norm dari matriks kovariansi errornya lebih kecil disbanding Kalman filter.
Updating Reservoir Models Using Ensemble Kalman Filter Sutawanir Darwis; AGUS YODI GUNAWAN; SRI WAHYUNINGSIH; NURTITI SUNUSI; ACENG KOMARUDIN MUTAQIN; NINA FITRIYATI
STATISTIKA: Forum Teori dan Aplikasi Statistika Vol 10, No 1 (2010)
Publisher : Program Studi Statistika Unisba

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.29313/jstat.v10i1.1007

Abstract

The Ensemble Kalman Filter (EnKF) has gain popularity as a methodology for real time updates ofreservoir models. A sample of models is updated whenever observation data available. Successfulapplication of EnKF to estimate reservoir properties has been reported. A flow modeling is missing inthis research area. This paper presents the applicability of EnKF in flow modeling for three cases:infinite reservoir, bounded reservoir and one dimensional composite reservoir. The solution of flowequation was derived and used as a modeling component of state space modeling of Kalman filterupdating formula. This three reservoir models shows that the EnKF methodology can be used forupdating the reservoir models.
Prediction of the Change Rate of Tumor Cells, Healthy Host Cells, and Effector Immune Cells in a Three-Dimensional Cancer Model using Extended Kalman Filter Fitriyati, Nina; Faizah, Salma Abidah; Sutanto, Taufik Edy
Jambura Journal of Biomathematics (JJBM) Volume 5, Issue 1: June 2024
Publisher : Department of Mathematics, Universitas Negeri Gorontalo

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.37905/jjbm.v5i1.24672

Abstract

In this study, we develop and implement the Extended Kalman Filter (EKF) to forecast the rate of change in tumor cells, healthy host cells, and effector immune cells within the Itik-Banks model. This novel application of EKF in cancer dynamics modeling aims to provide precise real-time estimations of cellular interactions, especially in constructing a new state space representation from the Itik-Banks model. We use a first-order Taylor series to linearize the model. The numerical simulations were performed to analyze the accuracy of this new state space with data from William Gilpin’s GitHub repository. The results show that the EKF predictions strongly align with actual data, i.e., in the prior and posterior steps for tumor and healthy host cells, there is a strong agreement between the predictions and the actual data. The EKF captures the oscillatory nature of the tumor and healthy host cell population well. The peaks and troughs of the predictions align closely with the actual data, indicating the EKF’s effectiveness in modeling the dynamic behavior of the tumor and healthy host cells. However, for effector immune cells, the oscillatory nature of the data in these cells gives rise to slight deviations. This represents a significant challenge in the future for updating the state space representations. Despite minor discrepancies, the EKF demonstrates a strong performance in both the training and testing data, with the posterior step estimates significantly improving the prior step accuracy. This study emphasizes the importance of data availability for accurate predictions, noting a symmetric Mean Absolute Percentage Error (sMAPE) of 35.92% when data is unavailable. Prompt correction with new data is essential to maintain accuracy. This research underscores the EKF’s potential for real-time monitoring and prediction in complex biological systems.
A Monte Carlo Simulation Study to Assess Estimation Methods in CFA on Ordinal Data Fitriyati, Nina; Wijaya, Madona Yunita
CAUCHY: Jurnal Matematika Murni dan Aplikasi Vol 7, No 3 (2022): CAUCHY: JURNAL MATEMATIKA MURNI DAN APLIKASI
Publisher : Mathematics Department, Universitas Islam Negeri Maulana Malik Ibrahim Malang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.18860/ca.v7i3.14434

Abstract

Likert-type scale data are ordinal data and are commonly used to measure latent constructs in the educational, social, and behavioral sciences. The ordinal observed variables are often treated as continuous variables in factor analysis, which may cause misleading statistical inferences. Two robust estimators, i.e., unweighted least square (ULS) and diagonally weighted least square (DWLS) have been developed to deal with ordinal data in confirmatory factor analysis (CFA). Using synthetic data generated in a Monte Carlo experiment, we study the behavior of these methods (DWLS and ULS) and compare their performance with normal theory-based ML and GLS (generalized least square) under different levels of experimental conditions. The simulation results indicate that both DWLS and ULS yield consistently accurate parameter estimates across all conditions considered in this study. The Likert data can be treated as a continuous variable under ML or GLS when using at least five Likert scale points to produce trivial bias. However, these methods generally fail to provide a satisfactory fit. Empirical studies in the field of psychological measurement data are reported to present how theoretical and statistical instances have to be taken into consideration when ordinal data are used in the CFA model.Keywords: confirmatory factor analysis, diagonally weighted least square, generalized least square, Likert data, maximum likelihood.
Web Traffic Anomaly Detection using Stacked Long Short-Term Memory Rahman, Fathu; Sutanto, Taufik Edy; Fitriyati, Nina
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol 3, No 2 (2021)
Publisher : Department of Mathematics, Faculty of Sciences and Technology, UIN Syarif Hidayatullah

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15408/inprime.v3i2.21879

Abstract

AbstractAn example of anomaly detection is detecting behavioral deviations in internet use. This behavior can be seen from web traffic, which is the amount of data sent and received by people who visit websites. In this study, anomaly detection was carried out using stacked Long Short-Term Memory (LSTM). First, stacked LSTM is used to create forecasting models using training data. Then the error value generated from the prediction on test data is used to perform anomaly detection. We conduct hyperparameter optimization on sliding window parameter. Sliding window is a sub-sequential data of time-series data used as input in the prediction model. The case study was conducted on the real Yahoo Webscope S5 web traffic dataset, consisting of 67 datasets, each of which has three features, namely timestamp, value, and anomaly label. The result shows that the average sensitivity is 0.834 and the average Area Under ROC Curve (AUC) is 0.931. In addition, for some of the data used, the window size selection can affect the sum of the sensitivity and AUC values. In this study, anomaly detection using stacked LSTM is described in detail and can be used for anomaly detection in other similar problems.Keywords: time-series data; sliding window; web traffic; window size. AbstrakSalah satu contoh deteksi anomali adalah mendeteksi penyimpangan perilaku dalam penggunaan internet. Perilaku ini dapat dilihat dari web traffic, yaitu jumlah data yang dikirim dan diterima oleh orang-orang yang mengunjungi situs web. Pada penelitian ini, deteksi anomali dilakukan menggunakan Long Short-Term Mermory (LSTM) bertumpuk. Pertama, LSTM bertumpuk digunakan untuk membuat model peramalan menggunakan data latih. Kemudian nilai error yang dihasilkan dari prediksi pada data uji digunakan untuk melakukan deteksi anomali. Kami melakukan optimasi hyperparameter pada parameter sliding window. Sliding window adalah data sub-sekuensial dari data runtun waktu yang digunakan sebagai input pada model prediksi. Studi kasus dilakukan pada dataset web traffic Yahoo Webscope S5 yang terdiri dari 67 dataset yang masing-masing memiliki tiga fitur yaitu timestamp, value, dan anomaly label. Hasil menunjukkan bahwa rata-rata sensitivitas sebesar 0.834 dan rata-rata Area Under ROC Curve (AUC) sebesar 0.931. Selain itu, untuk beberapa data yang digunakan, pemilihan window size dapat mempengaruhi jumlah dari nilai sensitivitas dan AUC. Pada penelitian ini, deteksi anomali menggunakan LSTM bertumpuk dijelaskan secara rinci dan dapat digunakan untuk deteksi anomali pada permasalahan lainnya yang serupa.Kata kunci: data runtun waktu; sliding window; web traffic; window size.
Variasi spasial dan temporal nilai-b pada gempa bumi di wilayah Sulawesi Tengah, Gorontalo, dan sekitarnya menggunakan metode robust fitting Fitriyati, Nina; Wijaya, Madona Yunita; Bisyri, M. Alvi
Majalah Ilmiah Matematika dan Statistika Vol 22 No 2 (2022): Majalah Ilmiah Matematika dan Statistika
Publisher : Jurusan Matematika FMIPA Universitas Jember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.19184/mims.v22i2.33817

Abstract

This study discusses variation in seismic and tectonic modeled by a Gutenberg-Richter relationship for earthquakes in the Central Sulawesi, Gorontalo, and surrounding areas using the Robust Fitting Method (RFM) with the weight function of Tukey’s bisquare. The declustering process on earthquake data is carried out using the Reasenberg equation. The values for both parameters are analyzed spatially and temporally. In the spatial analysis, the research area is divided into 43 grids. In the temporal analysis, the research area is divided into zone A and zone B. The data grouping is done using a sliding time window method, i.e., grouping 50 earthquake catalogs with 5 overlapping events. The results according to spatial analysis show that the b-values range from 0.38 – 1.19. Areas with low b-values (0.38 – 0.7) occur around the Palu-Koro Fault, i.e., Palu city, Malacca strait, and to Toli-Toli, and also in the northern region of Gorontalo, i.e., the subduction plate of the Sulawesi Sea. Meanwhile, high b-values (0.71 – 1.19) are in the Tomini Bay area which is an area with frequent occurrence of earthquakes but has the small potential to generate large-scale earthquakes. The results of the temporal b-value estimation in zones A and B range between values of 0.38 - 1.25. The b-values appear to decrease before the occurrence of major earthquakes in 1996 and 2018 in zone A. The b-values decreased before the occurrence of major earthquakes in 1990, 1991, 2000, and 2008 in zone B. However, the b-values cannot be used as a precursor before the big earthquake in 1997. Keywords: Tukey’s bisquare, Reasenberg equation, Gutenberg-Richter relationship, sliding time window, Robust Fitting Method. MSC2020: 86A15
Tabarru’ Fund Sharia Insurance Using The 2019 Mortality Table, Mortality Law and Cost of Insurance Method Wulandari, Fitria Sisca; Fauziah, Irma; Fitriyati, Nina
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 8 No. 4 (2023): Mathline: Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v8i4.542

Abstract

The sharia life insurance program has two ways of managing funds, namely involving a savings element and not involving a savings element. Programs that do not involve a savings element do not have a clear division of tabarru’ funds that must be paid participant so it is the company's job to calculate it . In calculating the percentage of tabarru' funds used method Cost of Insurance (COI) . The COI method is method for calculating tabarru’ funds  with using several parameters, namely mortality tables , investment value , management fees and discount factors . In this research, we will discuss how to obtain tabarru' funds using the 2019 Indonesian mortality table and the 2019 Indonesian mortality table with the Gompertz mortality law, Makeham mortality law and De Moivre mortality law. with method Cost of Insurance . Based on the case illustration, the results show that the tabarru' funds that must be paid by participants are directly proportional to the participant's age, management fees and insurance money, but inversely proportional to the investment value. Tabarru' funds will be greater if using the De Moivre mortality table so this can be a consideration for the company while the Makeham mortality table can be a consideration for participants.
Co-Authors . Mahmudi Aceng Komarudin Mutaqin Adjie, Dharma Syadhi Putra Agus Yodi Gunawan Alkadrie, Syarifah Syila Andrew Fiade Ayu Puji Rahayu Bisyri, M. Alvi Faizah, Salma Abidah Gina Isma Kusuma Handarbeni, Zalfa Talitha Inna, Suma Irma Fauziah Mahmudi Mahmudi Maysun, Maysun Muhammad Manaqib, Muhammad Nadilia, Nindita Nur Inayah Nuraini, Vita Nurmaleni Nurmaleni NURTITI SUNUSI Rahma, Chelsea Fatihah Rahman, Fathu Sari, Flori Ratna Sri Maliska Sri Wahyuningsih Sutanto, Taufik Edy Sutawanir Darwis Wijaya, Madona Yunita Wulandari, Fitria Sisca Yupinto, Ikhwal