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InPrime: Indonesian Journal Of Pure And Applied Mathematics
Published by Universitas Islam Negeri Syarif Hidayatullah Jakarta
ISSN : 26865335     EISSN : 27162478     DOI : 10.15408/inprime
Core Subject : Science, Education,
Computer Science & IT Mathematics
InPrime: Indonesian Journal of Pure and Applied Mathematics is a peer-reviewed journal and published on-line two times a year in the areas of mathematics, computer science/informatics, and statistics. The journal stresses mathematics articles devoted to unsolved problems and open questions arising in chemistry, physics, biology, engineering, behavioral science, and all applied sciences. All articles will be reviewed by experts before accepted for publication. Each author is solely responsible for the content of published articles. This scope of the Journal covers, but not limited to the following fields: Applied probability and statistics, Stochastic process, Actuarial, Differential equations with applications, Numerical analysis and computation, Financial mathematics, Mathematical physics, Graph theory, Coding theory, Information theory, Operation research, Machine learning and artificial intelligence.
Arjuna Subject : Matematika - Matematika Terapan
Articles 197 Documents
 15   16   17   18   19 
Stability Analysis and Optimal Control of Mathematical Model of Thypoid Fever Spread Siduppa, Muh. Nursyam; Toaha, Syamsuddin; Kasbawati, Kasbawati
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 1 (2023)
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.v5i1.27205

Abstract

AbstractTyphoid fever is an endemic disease caused by infection with Salmonella Typhi. The transmission of typhoid fever is through food and drink contaminated with Salmonella Typhi bacteria, which is excreted through the feces or urine of an infected person. The problem of typhoid fever is increasingly complex because of the increase in carrier cases, making it difficult for treatment and prevention efforts. This study develops a mathematical model for the control of typhoid fever, which consists of two equilibrium points, namely endemic and non-endemic equilibrium points. The endemic and non-endemic equilibrium point is asymptotically stable if it satisfies the condition given by the Routh-Hurwitz criterion. Optimal control theory is applied to the mathematical model by providing control through health campaigns, screening, and treatment to minimize the number of asymptomatic individuals, symptomatic individuals, and chronic carriers. The Pontryagin Minimum principle is used to determine the optimal control form. Numerical simulations are performed using the Forward-Backward Sweep Runge-Kutta method of order 4. The simulation results indicate a decrease in each infected subpopulation after applying optimal control for ten months. It is found that control in health campaigns has a more significant impact than control in screening and treatment in decreasing the number of asymptomatic and symptomatic individuals. The control of treatment effectively reduces infected individuals with symptoms of becoming chronic carriers. In conclusion, the most effective strategy in controlling the spread of typhoid fever is to simultaneously apply controls in the form of health campaigns, screening, and treatment.Keywords: health campaign; screening; treatment; optimal control; Pontryagin minimum principle; forward-backward sweep. AbstrakDemam tifoid merupakan penyakit endemik yang disebabkan oleh infeksi bakteri Salmonella Typhi. Proses penularan demam tifoid melalui makanan dan minuman yang  telah terkontaminasi bakteri Salmonella Typhi yang dikeluarkan melalui tinja maupun urin dari orang yang telah terinfeksi. Permasalahan tentang demam tifoid semakin kompleks karena meningkatnya kasus - kasus carrier, sehingga menyulitkan upaya pengobatan dan pencegahan. Model matematika yang dikembangkan memiliki dua titik kesetimbangan yaitu titik setimbang nonendemik dan titik setimbang endemik. Titik setimbang nonendemik dan endemik akan stabil asimtotik jika memenuhi kondisi yang diberikan oleh aturan Routh-Hurwitz. Teori kontrol optimal diterapkan pada model matematika dengan pemberian kontrol berupa kampanye kesehatan, screening dan pengobatan untuk meminimumkan jumlah individu asymptomatic, individu symptomatic dan carrier chronic. Penentuan bentuk kontrol optimal menggunakan prinsip Minimum Pontryagin. Simulasi numerik dilakukan dengan menggunakan metode Forward-Backward Sweep Runge-Kutta        orde 4. Berdasarkan hasil simulasi, terjadi penurunan disetiap subpopulasi terinfeksi setelah penerapan kontrol optimal selama 10 bulan. Kontrol berupa kampanye kesehatan memiliki pengaruh yang besar dibandingkan kontrol berupa screening dan pengobatan dalam menekan meningkatnya individu asymptomatic dan individu symptomatic. Penerapan kontrol berupa pengobatan sangat efektif dalam menekan individu terinfeksi dengan gejala menjadi individu carrier chronic.Kata Kunci: kampanye kesehatan; screening; pengobatan; kontrol optimal; prinsip minimum Pontryagin; forward-backward sweep. 2020MSC: 00A71, 92B05 
On Codes Over R and its Bounds of Some Kind of Block Repetition Codes in R Pandian, P Chella
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 4 No. 2 (2022)
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.v4i2.27239

Abstract

This correspondence determines the lower and upper bounds of the covering radius in some kind of block repetition codes over the finite ring R=Z_2 Z_*, where Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. For covering radii of binary and octonary block repetition code over  is also discussed. This leads to the convenient formulation of code and arrives at the bounds.Keywords: block repetition codes; covering radius; different weight; finite ring. AbstrakKorespondensi ini menentukan batas bawah dan batas atas dari jari-jari penutup suatu kode blok perulangan pada gelanggang hingga R=Z_2 Z_*, dengan Z_*=Z_2+vZ_2+v^2 Z_2, v^3=v. Dibahas juga jari-jari kode blok perulangan biner dan oktonari atas . Diperoleh rumus untuk kode dan batasnya.Kata Kunci: kode blok perulangan; penutup jari-jari;  berat yang berbeda; gelanggang hingga. 2020MSC: 11T71, 94B05, 11H71.
Moving Horizon State Estimation for Linear System with Application to Autonomous Vehicle Purnawan, Heri; Ilmi, Ulul; Faroh, Rifky Aisyatul; Ar Rizqi, Ahmad Bustanul Ali; Resmi, Fitroh
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 1 (2023)
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.v5i1.28313

Abstract

AbstractThis paper proposes moving horizon estimation (MHE) to estimate the state variables of autonomous vehicle linear systems under measurement noises. To solve the MHE optimization problem, quadratic programming is employed. The steering angle, yaw angle, and global position constraints of an autonomous vehicle are considered in the estimation design. According to the simulation results, it can be observed that although the longer MHE step can give better results compared to the shorter MHE step, the difference in the MHE step only slightly affects the estimated results. However, the longer MHE step can increase the computational time. Additionally, the proposed MHE scheme is compared to the Kalman filter (KF) estimator. Based on the obtained results, the KF gives a better estimation than the MHE, but this notion must be verified for other case studies.Keywords: autonomous vehicle; Kalman filter; linear system; MHE; quadratic programming. AbstrakPaper ini mengusulkan moving horizon estimation (MHE) untuk mengestimasi variabel keadaan sistem linier kendaraan otonom karena pengaruh noise pengukuran. Untuk menyelesaikan masalah optimasi MHE, digunakan pemrograman kuadratik. Kendala sudut kemudi, sudut yaw dan posisi global dari kendaraan otonom dipertimbangkan dalam desain estimasi. Dari hasil simulasi dapat diketahui bahwa meskipun langkah MHE yang lebih panjang dapat memberikan hasil yang lebih baik dibandingkan dengan langkah MHE yang lebih pendek, perbedaan langkah MHE hanya sedikit mempengaruhi hasil estimasi. Namun, langkah MHE yang semakin panjang dapat meningkatkan waktu komputasi. Selain itu, skema MHE yang diusulkan dibandingkan dengan estimator Kalman filter (KF). Berdasarkan hasil yang diperoleh, KF memberikan estimasi yang lebih baik daripada MHE, tetapi gagasan ini harus diverifikasi untuk studi kasus lainnya.Kata Kunci: kendaraan otonom; Kalman filter; sistem linier; MHE; pemrograman kuadratik. 2020MSC: 62P35, 65D19
Social Network Analysis of Twitter Users on BTS Topic Using Degree Centrality, Betweenness Centrality, and Closeness Centrality Adniati, Siti; Irwansyah, Irwansyah; Awanis, Zata Yumni
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 2 (2023)
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.v5i2.28722

Abstract

AbstractNowadays, a trademark is starting to be built through content on social media by involving influencers whose roles are increasingly needed in digital marketing. Hence, finding them on social media networks is an important thing. In brand recognition, BTS has a great influence where a brand they collaborate with gets an enthusiastic response from fans who participate in disseminating information and recommending it to others via Twitter. Therefore, this study aims to identify the potential influencer on the delivery of information on the topic of BTS on Twitter using social network analysis. Social network analysis applies the concept of graph theory where the potential influencer which is denoted by the central vertex is measured by measures of centrality, namely degree centrality, betweenness centrality, and closeness centrality. The result of the network consists of 649 vertices and 730 directed edges that form a disconnected and directed network with 67 weakly connected components. This study indicates that the influencers in the network can be fan accounts or fanbase accounts.Keywords: BTS; centrality; central vertex; influencer; social network analysis; Twitter. AbstrakDewasa ini, suatu merek dagang mulai dibangun  melalui konten di media sosial dengan melibatkan pemengaruh yang perannya semakin dibutuhkan pada pemasaran digital sehingga menemukan mereka di jaringan media sosial adalah suatu hal yang penting. Dalam pengenalan merek, BTS memberikan pengaruh yang besar dimana suatu merek yang berkolaborasi dengan mereka mendapat respon antusias dari penggemar yang ikut menyebarluaskan informasi dan merekomendasikannya kepada orang lain melalui Twitter. Oleh karena itu, penelitian ini bertujuan untuk mengidentifikasi pemengaruh potensial dalam penyampaian informasi pada topik BTS di Twitter menggunakan analisis jaringan sosial. Analisis jaringan sosial menerapkan konsep teori graf dimana simpul sentral diukur dengan ukuran sentralitas, yaitu sentralitas derajat, sentralitas keantaraan, dan sentralitas kedekatan. Diperoleh jaringan dengan 649 simpul dan 730 sisi berarah yang membentuk jaringan berarah tak terhubung yang terdiri atas 67 komponen terhubung lemah. Adapun hasil dari penelitian ini menunjukkan bahwa simpul sentral atau pemengaruh dalam jaringan dapat berupa akun personal dari pengemar (fan account) atau akun basis penggemar (fanbase).Kata Kunci: analisis jaringan  sosial, BTS,  pemengaruh , sentralitas, simpul sentral, Twitter. 2020MSC: 05C90, 91D30.
Research Trends in Mathematical Modeling Applied to Pandemic Cases: A Bibliometric Analysis Rosyida, Azma; Utami, Risqi; Arlinwibowo, Janu; Fatima, Gupita Nadindra; Himayati, Ade Ima Afifa
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 1 (2023)
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.v5i1.28873

Abstract

AbstractThe disease caused by the virus has caused a continuous pandemic worldwide since 2012. In order to slow down the rapid spread of the virus, many countries have taken recovery measures. This paper aims to analyze the trends of modeling pandemic cases in Scopus-indexed journals. The research method is a literature review using a bibliometric analysis approach starting from defining the keywords modeling' and ‘pandemic' in the Publish or Perish application with Google Scholar as the database. After narrowing the results by selecting the topic of modeling the pandemic problem it consisted of 200 articles in total. After that, the metadata was compiled using the Mendeley application, the VosViewer application was used to create a research trend visualization. The results obtained by bibliometric analysis show that the number of publications continues to increase. Which journals are published, which organizations and countries publish the most, how the evolution of perspective has changed since 2012, and which articles are most cited. We conclude that since the pandemic, there is a possibility of an evolution in the quality of publications.Keywords: bibliometric analysis; pandemic; mathematical model; Mendeley; Publish or Perish; Vosviewer. AbstrakPenyakit yang diakibatkan dari virus telah menyebabkan pandemi berkelanjutan di seluruh dunia sejak 2012. Untuk memperlambat penyebaran virus yang cepat, banyak negara telah mengambil langkah pemulihan. Tulisan ini bertujuan untuk menganalisis tren pemodelan kasus pandemi di jurnal terindeks Scopus. Metode penelitian adalah kajian pustaka dengan pendekatan analisis bibliometrik dimulai dari pendefinisian kata kunci ‘pemodelan’ dan 'pandemi' pada aplikasi Publish or Perish dengan database Google Scholar. Setelah dilakukan penyempitan hasil dengan pemilihan topik pemodelan masalah pandemi  maka total artikel menjadi 200 artikel. Setelah itu dilakukan kompilasi metadata menggunakan aplikasi Mendeley, aplikasi VosViewer digunakan untuk membuat visualisasi trend penelitian. Hasil yang diperoleh dengan analisis bibliometrik menunjukkan bahwa jumlah publikasi terus meningkat. Jurnal mana yang diterbitkan, organisasi dan negara mana yang paling banyak menerbitkan, bagaimana evolusi perspektif telah berubah sejak 2012, dan artikel mana yang paling banyak dikutip. Kami menyimpulkan bahwa sejak pandemi, ada kemungkinan terjadi evolusi kualitas publikasi.Kata Kunci: analisis bibliometrik; pandemi; model matematika; Mendeley; Publish or Perish; Vosviewer. 2020MSC: 00A71, 92B05.
Some Characteristics of the Prime Graph of Integer Modulo Groups Maulana, Muklas; Wardhana, I Gede Adhitya Wisnu; Switrayni, Ni Wayan; @ Ismail, Ghazali Semil
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 1 (2023)
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.v5i1.29014

Abstract

AbstractThe notion of the prime graph of a ring R was first introduced by Bhavanari, Kuncham, and Dasari in 2010. The prime graph of a ring R, denoted by PG(R) is a graph whose vertices are all elements of the ring, where two distinct vertices x and y are adjacent if and only if xRy = 0 or yRx = 0. In this paper, we study the forms and properties of the prime graph of integer modulo group, and some examples of the number of its spanning trees. In this paper, it is found that for all n, the maximum degree of vertices of PG(Z_n) is n-1 and the minimum degree of its vertices is 1. Then, we show that for all n, PG(Z_n) is neither a Hamiltonian graph nor an Eulerian graph. We also found some examples of the number of its spanning trees.Keywords: prime graph; spanning trees; Hamiltonian graph. AbstrakKonsep mengenai graf prima dari suatu gelanggang R pertama kali diperkenalkan oleh Bhavanari, Kuncham, dan Dasari pada tahun 2010. Graf prima dari suatu gelanggang R, yang dinotasikan dengan PG(R), adalah suatu graf yang simpul-simpulnya merupakan semua elemen dari gelanggang tersebut dengan dua buah simpul x dan y yang berbeda akan bertetangga jika dan hanya jika xRy = 0 atau yRx = 0. Di dalam penelitian ini, dikaji mengenai bentuk-bentuk dan sifat-sifat dari PG(Z_n), dan beberapa contoh dari banyak pohon pembangunnya. Pada penelitian ini, ditemukan hasil bahwa untuk setiap n, derajat maksimal dari simpul-simpul di PG(Z_n) adalah n-1 dan derajat minimum dari simpul-simpulnya adalah 1. Hasil selanjutnya yaitu, untuk setiap n, PG(Z_n) bukan merupakan suatu graf Hamiltonian atau graf Eulerian. Ditemukan juga beberapa contoh dari banyaknya pohon pembangun dari PG(Z_n).Kata Kunci: graf prima; pohon pembangun; graf Hamiltonian. 2020MSC:  05E16, 05C90, 20C05
The Structures of Non-Coprime Graphs for Finite Groups from Dihedral Groups with Regular Composite Orders Aulia, Sita Armi; Wardhana, I Gede Adhitya Wisnu; Irwansyah, Irwansyah; Salwa, Salwa; Misuki, Wahyu Ulyafandhie; Nghiem, Nguyen Dang Hoa
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 2 (2023)
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.v5i2.29018

Abstract

AbstractFor any finite group, the non-coprime graph of the group is a graph with vertices consisting of all non-identity elements of the group. Two different vertices are considered adjacent if their orders are not coprime, meaning their greatest common divisor (gcd) is not equal to one. Misuki provides the structure of the non-coprime graph for the dihedral group when the order is a prime power. We establish a more general property for cases where the order of the group is a regular composite number, discovering that the structure of the non-coprime graph for a dihedral group can be partitioned into some number of complete subgraphs.Keywords: dihedral group; disjoint subgraph; non-coprime graph. AbstrakUntuk sebarang grup hingga, graf non-coprime dari grup tersebut adalah graf dengan simpul yang terdiri dari semua elemen non-identitas dari grup tersebut. Dua simpul yang berbeda dianggap bertetangga jika orde mereka tidak saling prima, artinya pembagi terbesar bersama (gcd) mereka tidak sama dengan satu. Misuki memberikan struktur graf non-coprime untuk grup dihedral ketika ordenya adalah pangkat prima. Pada studi ini didapatkan sifat yang lebih umum ketika orde grup adalah bilangan komposit biasa. Didapatkan juga bahwa struktur graf non-coprime dari grup dihedral dapat dipartisi menjadi beberapa subgraf lengkap.Kata Kunci: graf non-koprima; grup dihedral; subgraph disjoin. 2020MSC: 05C25, 05C69, 20D60.
The Strong 3-Rainbow Index of Graphs Containing Three Cycles Awanis, Zata Yumni
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 1 (2023)
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.v5i1.29133

Abstract

AbstractThe concept of a strong k-rainbow index is a generalization of a strong rainbow connection number, which has an interesting application in security systems in a communication network. Let G be an edge-colored connected graph of order n, where adjacent edges may be colored the same. A rainbow tree in G is a tree whose edges have distinct colors. For an integer k with 2≤k≤n, the strong k-rainbow index srx_k (G) of G is the minimum number of colors needed to color all edges of G so that every k vertices of G are connected by a rainbow tree of minimum size. We focus on k=3. It is clear that srx_3 (G)≤‖G‖, where the upper bound is sharp since the srx_3 of a tree equals its size. Hence, we are interested in studying how the srx_3 of a tree changes if we add some edges connecting two nonadjacent vertices in the tree. This paper is focused on graphs containing three cycles. We first determine a sharp upper bound of the srx_3 of graphs containing exactly three edge-disjoint cycles. We also determine the exact values of srx_3 of theta graph θ(a_1,a_2,a_3) for certain values of a_1, a_2, and a_3.Keywords: cycle; rainbow coloring; rainbow Steiner tree; theta graph; tree. AbstrakKonsep indeks pelangi-k kuat merupakan perumuman dari bilangan terhubung pelangi kuat yang memiliki aplikasi menarik dalam sistem keamanan jaringan komunikasi. Misalkan G adalah suatu graf terhubung berorde n yang memiliki suatu pewarnaan sisi, dimana dua sisi bertetangga boleh memiliki warna yang sama. Pohon pelangi di G adalah pohon yang setiap sisinya memiliki warna berbeda. Untuk suatu bilangan bulat k dengan 2≤k≤n, indeks pelangi-k kuat srx_k (G) graf G adalah banyak warna minimum yang dibutuhkan untuk mewarnai semua sisi di G sehingga setiap k titik di G dihubungkan oleh suatu pohon pelangi berukuran minimum. Kami fokus pada k=3. Jelas bahwa srx_3 (G)≤‖G‖, dimana batas atas ini merupakan batas ketat karena srx_3 pohon sama dengan ukurannya. Karena itu, kami tertarik untuk mempelajari bagaimana srx_3 pohon berubah jika ditambahkan beberapa sisi yang menghubungkan dua titik tidak bertetangga di pohon tersebut. Artikel ini difokuskan pada graf yang memuat tiga siklus. Pertama, kami menentukan batas atas ketat srx_3 graf yang memuat tepat tiga siklus saling lepas sisi. Kami juga menentukan nilai eksak srx_3 graf theta θ(a_1,a_2,a_3 ) untuk beberapa nilai a_1, a_2, dan a_3 tertentu.Kata Kunci: siklus; pewarnaan pelangi; pohon Steiner pelangi; graf theta; pohon. 2020MSC: 05C05, 05C15, 05C38, 05C40.
An Optimal Control Analysis of Dengue Fever Ilmayasinta, Nur; Febriyanti, Rahma; Prafianti, Rayinda Aseti; Zakiyah, Nabila Syarifah
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 2 (2023)
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.v5i2.30392

Abstract

AbstractDengue fever is one of the most infectious diseases in the world, according to data issued by the World Health Organization in 2014. It is responsible for a huge number of deaths each year around the world, particularly in tropical nations. The dengue virus (DENV) causes dengue fever, which is spread by the female Aedes aegypti mosquito. We provide a mathematical model of dengue fever transmission through hospitalization with optimal management in this paper. Before being simulated in MATLAB, this optimum control problem is numerically resolved. Vaccination, pesticide use, and prevention are all examples of optimal control in this study. The simulation results demonstrate that dengue infection can be considerably reduced by vaccination, pesticide use, and prevention.Keywords: Dengue fever; Mathematical modelling; Optimal control. AbstrakDemam berdarah adalah salah satu penyakit paling menular di dunia, menurut data yang dikeluarkan oleh Organisasi Kesehatan Dunia pada tahun 2014. Penyakit ini menyebabkan banyak kematian setiap tahun di seluruh dunia, terutama di negara-negara tropis. Virus dengue (DENV) menyebabkan demam berdarah, yang disebarkan oleh nyamuk Aedes aegypti betina. Kami menyediakan model matematis penularan demam berdarah melalui rawat inap dengan penatalaksanaan optimal dalam makalah ini. Masalah kontrol optimal ini diselesaikan secara numerik sebelum disimulasikan di MATLAB. Vaksinasi, penggunaan pestisida, dan pencegahan merupakan contoh pengendalian yang optimal dalam penelitian ini. Hasil simulasi menunjukkan bahwa infeksi dengue dapat dikurangi dengan vaksinasi, penggunaan pestisida, dan pencegahan.Kata Kunci: Demam berdarah; Pemodelan matematika; Kontrol optimal. 2020MSC: 00A71, 92B05.
The Alpha Power Transformed Logistic Distribution: Properties, application and VaR Estimation Iwuji, Anayo Charles; Oruh, Ben Ifeanyichukwu; Nwabueze, Joy Chioma; Okereke, Emmanuel Wilfred
InPrime: Indonesian Journal of Pure and Applied Mathematics Vol. 5 No. 1 (2023)
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.v5i1.31035

Abstract

AbstractIn this paper, a new three-parameter distribution, which is a member of the Alpha Power Transformed Family of distributions, is introduced. The new distribution is a generalization of the logistic model called the alpha power transformed logistic (APTL) distribution. Some mathematical properties of the new distribution like moments, quantile function, median, skewness, kurtosis, Rényi entropy, and order statistics are discussed. The parameters of the distribution are estimated using the maximum likelihood estimation method and a simulation study is performed to investigate the effectiveness of the estimates. The usefulness and flexibility of the APTL distribution in modelling financial data are investigated using two portfolio stock indices, namely the NASDAQ and New York stock indices, both from the United States stock market. Based on the model selection criteria, we are able to establish empirically that the APTL distribution is the best for modelling the two data sets, among the various distributions compared in the study. For each of the data, the quantile value-at-risk estimates for the APTL distribution give the smaller expected portfolio loss at high confidence levels in comparison to those of the other distributions.Keywords: Alpha power transformed family of distributions; logistic distribution; maximum likelihood estimation; portfolio investments; value-at-risk. AbstrakPada artikel ini, diperkenalkan distribusi baru dengan tiga parameter yang merupakan anggota dari keluarga distribusi Alpha Power Transformed. Distribusi baru ini merupakan generalisasi dari model logistik yang disebut distribusi Alpha Power Transform Logistics (APTL). Selain itu, dibahas pula beberapa sifat matematika dari distribusi tersebut yaitu momen, fungsi kuantil, median, kemiringan, kurtosis, entropi Rényi, dan statistik terurut. Parameter distribusi diestimasi menggunakan metode maximum likelihood estimation dan studi simulasi dilakukan untuk menyelidiki keefektifan estimasi. Kegunaan dan fleksibilitas distribusi APTL dalam pemodelan data keuangan diselidiki menggunakan dua indeks saham portofolio dari pasar saham Amerika Serikat yaitu indeks saham NASDAQ dan New York. Berdasarkan kriteria pemilihan model, secara empiris, dihasilkan bahwa APTL adalah distribusi terbaik untuk memodelkan dua set data di antara berbagai distribusi yang dibandingkan pada penelitian ini. Untuk setiap data, estimasi kuantil value-at-risk untuk distribusi APTL memberikan kerugian portofolio yang diharapkan lebih kecil dengan tingkat kepercayaan tinggi dibandingkan dengan distribusi lainnya.Kata Kunci: distribusi dari keluarga Alpha power transformed; distribusi logistik; maximum likelihood estimation; investasi portofolio; value-at-risk. 2020MSC: 62E10.

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