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Yuni Yulida
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Mathematics Department, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat University. Jl. A. Yani KM.35.8 Banjarbaru, Kalimantan Selatan
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INDONESIA
Epsilon: Jurnal Matematika Murni dan Terapan
Published by Universitas Lambung Mangkurat
ISSN : 19784422     EISSN : 26567660     DOI : http://dx.doi.org/10.20527
Core Subject : Science, Engineering,
Decision Sciences, Operations Research & Management Transportation
Jurnal Matematika Murni dan Terapan Epsilon is a mathematics journal which is devoted to research articles from all fields of pure and applied mathematics including 1. Mathematical Analysis 2. Applied Mathematics 3. Algebra 4. Statistics 5. Computational Mathematics
Arjuna Subject : Matematika - Matematika Terapan
Articles 10 Documents
 1 
Search results for , issue "Vol 18, No 2 (2024)" : 10 Documents clear
SIFAT-FK RUANG BARISAN CESARO ORLICZ Haryadi, Haryadi -
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13899

Abstract

The Cesaro sequence space , ( , which is the FK-space, has been generalized to the Cesaro-Orlicz sequence space . This prompted the study of several properties in  that have been known in . In this paper, the properties of completeness and FK-properties in the Cesaro-Orlicz space are discussed. For this discussion, a modular approach is used. The results of the study show that the space   is a convex modular space. This sequence space is also complete to the Luxemburg norm and has K-properties. Furthermore, this space is a BK-space. These results can be used to study the Kothe-Toeplitz dual, which is an important part of the transformation of the infinite matrix
PENDEKATAN BAYESIAN MARKOV CHAIN MONTE CARLO (MCMC) METROPOLIS-HASTINGS PADA PEMODELAN KLAIM ASURANSI KESEHATAN Lestia, Aprida Siska; Idris, Mochammad
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13872

Abstract

The distribution of health insurance claims that tend to be asymmetric and have heavy tails, requires a method that can offer more flexible and robust solutions than traditional frequentist approaches, such as the Bayesian Method. The advantage of this method lies in its ability to comprehensively account for uncertainty in parameter estimation, thereby producing a posterior distribution that can capture complex pattern of claim data. This study aims to apply the Bayesian approach with the Markov Chain Monte Carlo (MCMC) Metropolis-Hastings method in modeling health insurance claims. The claim data used are divided into outpatient and inpatient claims, with the lognormal distribution fitting proven to be the most appropriate for both types of claims. Risk estimation through Value at Risk (VaR) and Conditional Tail Expectation (CTE) using the Bayesian approach showed more moderate results compared to empirical estimates, indicating that this approach can reduce risk overestimation
SEPUTAR ALJABAR ENVELOPING UNIVERSAL DARI ALJABAR LIE FROBENIUS BERDIMENSI 4 Kurniadi, Edi; Badrulfalah, Badrulfalah; Parmikanti, Kankan
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13798

Abstract

Setiap aljabar Lie mempunyai aljabar enveloping universal dan bersifat tunggal. Dalam penelitian ini, dipelajari aljabar enveloping universal dari suatu aljabar Lie Frobenius berdimensi 4. Tujuannya adalah untuk membuktikan bahwa aljabar enveloping universal dari suatu aljabar Lie Frobenius berdimensi 4 bersifat primitif. Pertama-tama, dikonstruksi suatu basis untuk aljabar enveloping universal menggunakan Teorema Poincare-Birkhoff-Witt untuk menentukan secara eksplisit aljabar enveloping universalnya dan langkah kedua, menentukan karakteristik aljabar enveloping universal hasil konstruksi. Hasil dalam penelitian ini menunjukkan bahwa setiap aljabar enveloping universal dari aljabar Lie Frobenius berdimensi 4 senantiasa bersifat primitif.
ANALISIS SURVIVAL PASIEN RAWAT INAP DIABETES MELITUS TIPE-II MENGGUNAKAN METODE KAPLAN MEIER DI RSUD KUALA PEMBUANG Ananda, Rosa; Salam, Nur; Noor, Meitria Syahadatina
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13170

Abstract

Diabetes mellitus (DM) is a chronic metabolic condition characterized by high blood sugar levels caused by insulin deficiency. According to data from the International Diabetes Federation, as many as 80% of diabetes patients worldwide live in developing countries, one of which is Indonesia. Indonesia ranks fifth in the world for the highest number of diabetes patients, including the Kuala Pembuang area with a rate of 1.1%. This study aims to determine whether there are differences in each variable affecting the length of hospitalization for patients with type-II diabetes mellitus at RSUD Kuala Pembuang, and to determine this, survival analysis methods such as the Kaplan-Meier method and Log Rank Test were used. Secondary data from the medical records of RSUD Kuala Pembuang were utilized. The data used during the research over the period of 2020 included age, gender, blood glucose levels, comorbidities, and blood pressure. The result of this study is that female patients over the age of 45 are more numerous than male patients. Patients with comorbidities have blood pressure of 140/90 mmHg or higher, as well as inpatient blood glucose levels of 200 mg/dL or higher. Log Rank test analysis shows a significant gap between age groups and comorbidities.
ANALISIS CONDITIONAL VALUE AT RISK PORTOFOLIO SAHAM DENGAN COPULA CLAYTON Karlina, Sela; Sulistianingsih, Evy; Satyahadewi, Neva
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13261

Abstract

Conditional Value at Risk (CVaR) is known as a risk measurement tool to estimate losses in investing. Financial data tends not to be normally distributed so that the flexible Copula method can be used to analyze financial data without requiring the assumption of normality. This study aims to analyze the CVaR of a stock portfolio with Clayton's Copula. The study began with collecting daily stock closing price data for the period October 3, 2022 to November 3, 2023. After the data was collected, the return value of the closing stock price was calculated. Furthermore, autocorrelation and heteroscedasticity tests were carried out on the closing stock price return data. Then, the Kendall's Tau correlation was calculated to obtain the Clayton Copula parameters. After that, the stock weights in the portfolio were calculated using the Mean Variance Efficient Portfolio (MVEP) method and new return data was generated using the Clayton Copula parameters. Furthermore, the portfolio return was calculated to obtain the VaR value of the formed portfolio. Then, it was repeated by generating data up to the VaR calculation 1000 times to obtain the average value of the portfolio VaR. Then, the same thing was done to CVaR. The results of the CVaR analysis of the stock portfolio with Copula Clayton on the two stocks, namely PT Aneka Tambang Tbk (ANTM) and PT Timah Tbk (TINS), obtained losses of 3.04%, 3.56%, and 4.57% with a confidence level of 90%, 95%, and 99%. This value indicates the percentage of investment risk that may be obtained in the next one-day period. This shows that the higher the level of confidence, the greater the CVaR value will be.
ALGORITMA KRUSKAL UNTUK MENYELESAIKAN MASALAH OPTIMASI DISTRIBUSI JARINGAN LISTRIK DI PLN UP3 CIMAHI Sartika, Euis; Lusiani, Anie; Suhartini, Ida; Nuryati, Neneng
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13256

Abstract

The addition of new houses in the Kota Mas Cimahi housing complex has triggered an increase in the need for electricity distribution installations. To optimize the electricity distribution network, in this case minimizing the installation of electrical cables, an application is needed that can optimize the installation of electrical cables, namely the Kruskal algorithm which is an algorithm for finding the minimum spanning tree value on a weighted graph. In this study, two methods will be used, namely the manual method and the POM-QM for Windows software to help solve the minimum spanning tree problem. This study's goal is to identify the Kota Mas Cimahi housing complex's energy distribution network model's graph structure and determine a minimum spanning tree solution with POM-QM for Windows software and the Kruskal technique done by hand. In order to gather data for this study, PLN was the primary and secondary source Cimahi UP3. The distribution data for the electricity cable network is arranged in the form of a network image. By representing the electricity distribution network in the form of a graph, the minimum spanning tree is then obtained, and the solution to the MST (Minimum Spanning Tree) problem uses the Kruskal algorithm and TORA software. The results of the study showed that the minimum spanning tree cable length which was originally 1424.61 meters, after using the Kruskal algorithm manually became 1258.05 meters and also by using the POM-QM for Windows software obtained a minimum result of 1258.05 meters, so it can be concluded that there is a cable length efficiency of 11.69%.
PENGGUNAAN RUMUS STIRLING DAN FUNGSI PEMBANGKIT MOMEN PADA PROSES PEMBUKTIAN DISTRIBUSI NORMAL SEBAGAI PENDEKATAN DISTRIBUSI BINOMIAL Santosa, Raden Gunawan; Haryono, Nugroho Agus
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.14164

Abstract

Research in mathematics and statistics can be categorized into two main types: analytical-theoretical research and applied-practical research, both of which make significant contributions to statistical analysis. This research is particularly relevant to the analysis of large-scale binary variables, where the binomial distribution is often used as the basis for computation. In such cases, the normal distribution can serve as an approximation to the binomial distribution, reducing the complexity of calculations. This study aims to demonstrate that the normal distribution can be used as an approximation for the binomial distribution. Two proof methods are presented: one utilizing the moment-generating function and the other employing Stirling's formula. The methodology involves a literature review by gathering and analyzing various relevant references. The findings indicate that as the value of ???? n increases, the difference between calculations using the binomial and normal distributions approaches zero exponentially.
ESTIMASI VALUE AT RISK (VAR) DENGAN METODE MONTE CARLO UNTUK MENGUKUR RISIKO KERUGIAN PETANI KETIMUN DI KABUPATEN KAPUAS HULU Arsanti, Resti; Sulistianingsih, Evy; Septiawan, Anggi
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.11433

Abstract

Measurement of an estimated loss needs to be done by every business actor. The measurement can be done by calculating the Value at Risk (VaR). VaR is an estimate of the maximum loss that is assumed to be experienced in a certain period at the confidence interval used. Three forms of calculation methods can be used in calculating VaR estimates, namely parametric methods, methods with Monte Carlo simulation approaches, and Historical Simulation Methods. The data used is the average monthly producer price data of cucumber commodities with a period range starting from January 2020 to December 2022. The VaR calculation method in this analysis is the Monte Carlo simulation approach method which has the condition that the return data from the average producer price is normally distributed. The results of the VaR calculation with the Monte Carlo simulation method show that after generating return data with repetition 1000 times for an investment of 1 rupiah, the probability that cucumber farmers in Kapuas Hulu Regency, West Kalimantan Province will experience maximum losses is 5.79% for a confidence level of 80%, 9.08% for a confidence level of 90%, 11.39% for a confidence level of 95%, and 14.81% for a confidence level of 99%.
SOFT GROUPOID AND ITS PROPERTIES Abdurrahman, Saman
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.13781

Abstract

A groupoid is a generalized form of the concept of a group, achieved by omitting the properties of associativity, identity, and inverses. In this paper, we introduce the concept of a soft groupoid, which serves as a generalization of the soft group. We define and explore the properties of intersection, AND, and union on soft groupoids and soft subgroupoids. Furthermore, we explore the properties of these operations when applied to collections of soft subgroupoids derived from a given soft subgroupoid.
PENERAPAN ALGORITMA HILL CIPHER DAN PERMUTASI PADA SISTEM KRIPTOGRAFI POLYALPHABETIC Lukmaini, Sindi; Wira Tama, Yanuar Bhakti; Nugraheni, Kartika
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN (EPSILON: JOURNAL OF PURE AND APPLIED MATHEMATICS) Vol 18, No 2 (2024)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v18i2.12845

Abstract

TTechnological advances have a great influence on facilitating long-distance communication, one of which is exchanging messages. The security of a message is an important aspect of protecting sensitive information. Cryptography is a branch of science that aims to maintain the confidentiality, integrity, and authenticity of messages in communication. One of the cryptographic methods used is Hill Cipher, which converts plaintext into ciphertext using a key matrix, but Hill Cipher is vulnerable to cryptanalysis attacks, especially if the key matrix is not chosen properly. Based on these problems, this research was conducted by applying the Hill Cipher algorithm with permutation as an additional layer of security. This study aims to analyze the effect of the message and key matrix on the performance of computation time in the encryption and decryption process of Hill Cipher combined with permutation, where the message characters are limited to 26 alphabetic characters and the use of Hill block length and permutation techniques is set at 5 characters. The simulation results show the average performance of computation time on the encryption and decryption process is 0.000083199 seconds and 0.000113493 seconds for a message with 707 characters. The key matrix used must be invertible, and the performance of computation time on encryption and decryption with different keys is 0.000094817 seconds and 0.00025938 seconds.

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