Jurnal Matematika, Statistika dan Komputasi
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The Generalized Riemann Integral
Get PDFRiemann integration theory integrates functions on a bounded interval as a Riemann sum approach (integral) where the fineness of the partitions is controlled by a number (norm) of the partition. In Generalized Riemann integral theory, the Riemann sum approach of functions is controlled by a gauge on tagged partition so that enabling integrating functions with much larger collections. Therefore, the theorems that apply to Generalized Riemann integral theory have differences in their hypotheses and conclusions. In this paper, theory of Generalized Riemann integral is studied by giving some examples of functions that are Generalized Riemann integrable such that they are not Riemann integrable; and proving some theorems that apply in this theory. The functions are integrable by constructing a gauge on the tagged partition of the interval such that the Riemann sum of the function is very close to some real number. Functions defined on a bounded interval that are Generalized Riemann integrable such that they are or not Riemann integrable have the general form of the function: a function f on [a,b] is continuous on [a,b]\Z and discontinuous on Z, where Z is a null set. Moreover, an unbounded function f on [a,b] is integrable, if the set Z where f is unbounded on Z is a countable set. Furthermore, these two criteria can be extended to infinite intervals, i.e. a function defined on an infinite interval can be Generalized Riemann integrable such that it is not Riemann integrable, if the set of discontinuous and unbounded points of the function is a null set. A sequence of integrable functions on an interval I that converges to a function on I, satisfies that this limit function is integrable if it satisfies that the existence of the dominating functions.Teori integrasi Riemann mengintegralkan fungsi pada interval terbatas sebagai pendekatan jumlah Riemann (integral) dimana kehalusan partisi-partisi dikendalikan oleh sebuah bilangan (norm) dari partisi. Pada teori integral Riemann Diperumum, pendekatan jumlah Riemann dari fungsi dikendalikan oleh gauge pada partisi tag sehingga memampukan mengintegralkan fungsi-fungsi dengan koleksi yang jauh lebih besar. Oleh karena itu, teorema-teorema yang berlaku pada teori integral Riemann Diperumum mempunyai perbedaan dalam hipotesis dan kesimpulannya. Pada makalah ini, dikaji teori integral Riemann Diperumum dengan memberikan beberapa contoh fungsi-fungsi yang terintegralkan Riemann Diperumum sedemikian sehingga tidak terintegralkan Riemann; dan membuktikan beberapa teorema yang berlaku dalam teori ini. Fungsi-fungsi tersebut dapat terintegralkan dengan mengkonstruksi sebuah gauge pada partisi tag dari suatu interval sehingga jumlah Riemann dari fungsi menuju (sangat dekat) ke suatu bilangan real. Fungsi-fungsi yang didefinisikan pada sebuah interval terbatas yang terintegralkan Riemann Diperumum sedemikian sehingga tidak terintegralkan Riemann memiliki bentuk umum fungsi: fungsi f pada [a,b] adalah kontinu pada [a,b]\Z dan diskontinu pada Z, dimana Z adalah suatu himpunan null. Kemudian sebuah fungsi tidak terbatas f pada [a,b] dapat terintegralkan, jika himpunan Z dimana f tidak terbatas pada Z adalah sebuah himpunan terhitung (countable). Lebih lanjut, dari kedua kriteria ini dapat diperluas ke interval tidak berhingga, yakni suatu fungsi yang didefinisikan pada interval tidak berhingga dapat terintegralkan Riemann Diperumum sedemikian sehingga tidak terintegralkan Riemann, jika himpunan-himpunan titik-titik diskontinu dan tidak terbatas dari fungsi adalah suatu himpunan null. Barisan fungsi-fungsi yang terintegralkan pada suatu interval I yang konvergen ke sebuah fungsi pada I, memenuhi bahwa fungsi limit ini adalah terintegralkan jika memenuhi adanya fungsi dominasi
Cross-Correlation Analysis in Evaluating Spatio-Temporal Data Dependence of Climate Variables Through the GSTAR Model
Get PDFClimate change analysis requires an approach which is capable to accommodate the dynamics of relationships between climatological variables in space and time dimensions. Temperature, humidity, and rainfall vary temporally and exhibit spatial dependence across locations. This study applies the Generalized Space-Time Autoregressive (GSTAR) model to analyze the spatial and temporal dependence patterns of climate variables in Tasikmalaya. The novelty of this study lies in the cross-correlation analysis of climate variables using actual data and model estimation results. This analysis can be used to assess how well the GSTAR model maintains the spatio-temporal dependence pattern. GSTAR modeling is performed by applying the Three-Stage Iterative Box-Jenkins method to space-time data. The results indicate that GSTAR(3;1,1,1) is the best-fitting model. Furthermore, this model consistently captures historical data patterns and accommodates the dynamic dependencies between climate variables at the two observation locations. The results show that the GSTAR(3;1,1,1) model consistently represents historical data patterns and accommodates the dynamics of relationships between meteorological variables at the observed locations. This finding confirms that the GSTAR model is an effective approach for capturing the spatio-temporal dependence of climate data, particularly in preserving the natural relationship patterns in actual data
Log Normal Regression and its Application
Get PDFLog Normal Regression and its Application
Ni Luh Sri Diantini1, Calvin Riswandi1
1Statistics Department Matana University
Email: [email protected],
[email protected]
Received: 19 December 2024, revised: 17 March 2025, accepted: 24 March 2025
Abstract
The log-normal distribution represents a type of continuous probability distribution that is characterized by a positive skew, which signifies a long tail on the right. A log-normal distribution describes a statistical distribution of values that have been logarithmically transformed from a related normal distribution. In situations where predictor variables affect positive outcomes, log-normal regression becomes significant. This research will construct a regression model that utilizes a continuous response variable following a log-normal distribution, known as log-normal regression (LNR). The purpose of developing the LNR model is to overcome the assumptions in classical regression that are often unmet, such as normality, since not all data can full fill these assumptions. Therefore, need an alternative method that does not require the normality assumption. One method that can be employed is a regression with a specific distribution approach, such as the log-normal distribution, known as log-normal regression. The LNR model will be developed through the maximum likelihood estimation (MLE) approach to achieve parameter estimation using a numerical method based on the Newton-Raphson iteration. Following this, hypothesis testing will be performed using the maximum likelihood ratio test (MLRT) and a partial test that employs the Wald test. The ultimate objective of this research is to illustrate how to apply the proposed LNR model to real data. LNR model will be applied to analysis the number of poor people in Indonesia, examining the factors that contribute to this issue. The results obtained in this study that variables human development index, unemployment rate, percentage of gross regional domestic product, and minimum wage in provinces influencing significance the number of poor people in Indonesia
Optimization of Long Short Term Memory Model for Gold Price Prediction Using Adaptive Moment Estimation
Get PDFThe era of globalization and rapidly evolving economic dynamics place the financial sector at the center of attention for market participants and investors. Financial instruments such as gold play a crucial role as hedging tools and portfolio diversification, yet face significant challenges due to complex and unpredictable price fluctuations. Artificial intelligence technology, particularly Long Short Term Memory (LSTM) models and Adaptive Moment Estimation (ADAM), offers relevant solutions for predicting financial asset prices with strong temporal fluctuations, such as gold prices. This research aims to optimize the LSTM model using the ADAM technique to enhance the accuracy of gold price predictions. The research findings indicate that the LSTM model optimized with ADAM can provide highly accurate gold price predictions with low error rates. The LSTM model used has 3 layers with 128, 64, and 32 units, and uses 100 epochs in the model training process. At the 100th epoch, the final loss obtained was 0,000336. Model evaluation results showed a MAPE of around 0,0108 or 1,08% an accuracy rate of about 98,92%, and a low loss value of 0,00025
Gutman, Sombor, and Harmonic Indices of Unit Graphs in The Integer Ring Modulo with A Specific Order
Get PDFThe ring of integers modulo is an algebraic structure that plays an important role in various fields, such as number theory, cryptography, and number system modeling. This structure also has a strong connection to graph representation, especially in the formation of unit graphs. This research focuses on the analysis of unit graphs formed from modulo integer algebras of a certain order, which aims to formulate the general form of topological indices, namely Gutman, Sombor, Reduced Sombor, Average Sombor, and Harmonic. The research considers two cases: the ring of integer modulo and , where is an odd prime number. The results show that each index has a unique and specific mathematical pattern according to its unit graph order. These findings provide a deeper understanding of the topological and combinatorial properties of unit graphs, which may help in generalizing their topological indices
Stock Price Forecasting Using Autoregressive With Exogenous Variable Support Vector Regression (ARX – SVR)
Get PDFStock prices move fluctuate continuously and dynamically at all times, so stock price predictions are needed to maximize profits for investors and avoid losses due to the characteristic of stock prices. Autoregressive (AR) model is a forecasting method and has weaknesses against nonlinear patterns. In addition to using linear modeling, forecasting stock prices can use the Support Vector Regression model which offers a global optimal solution that works with data maps to high-dimensional spaces and has good performance with time series problems. The addition of exogenous variables X to the model can also improve forecasting accuracy. Forecasting will be done using significant lags as input to Support Vector Regression. The modeling results show that the ARX-SVR model with X as an outlier exogenous variables provides the best out-of-sample data forecasting results for the case study of stock closing price forecasting. This model provides forecasting results with Symmetric Mean Absolute Percentage Error (sMAPE) 5.382430%
Bilangan Kromatik Graf Hasil Operasi Korona Sisi Graf Siklus dan Graf Bintang
Get PDFOne of the concepts in graph theory that can be analyzed is chromatic numbers of a graph and operation of two graphs. There are various kinds of operations of two graphs, one of which is the corona edge operation. This research aims to determine the chromatic number of the edge corona operation of graph Cn*K1,m and K1,m*Cn, where Cn is a cycle graph and K1,m is a star graph. The chromatic number is determined based on the pattern formed from several n and m values. The results of this research show that the chromatic number of the edge corona operation of graph Cn*K1,m is 4 for n= 3, 4, ... k and m=1, 2, 3, ..., l.
The chromatic number of the edge corona operation of graph K1,m*Cn is 5 if n is odd number. and is 4 if n is even number.Salah satu konsep dalam teori graf yang dapat diteliti adalah bilangan kromatik dari suatu graf dan operasi dari dua graf. Terdapat berbagai macam operasi dari dua graf salah satunya adalah operasi korona sisi. Penelitian ini bertujuan untuk mengetahui bilangan kromatik graf hasil operasi korona sisi graf Cn*K1,m dan K1,m*Cn , di mana Cn adalah graf siklus dan K1,m adalah graf bintang. Bilangan kromatik ditentukan berdasarkan pola yang terbentuk dari beberapa nilai n dan m. Dari penelitian ini diperoleh hasil bahwa bilangan kromatik graf hasil operasi korona sisi graf Cn*K1,m adalah 4 untuk n= 3, 4, ... k dan m=1, 2, 3, ..., l. Bilangan kromatik graf hasil operasi korona sisi graf K1,m*Cn adalah 5 jika n merupakan bilangan ganjil, dan adalah 4 jika n merupakan bilangan genap.
 
The Second Mean Value Theorem for Integrals
Get PDFThis article discusses the Second Mean Value Theorem for integrals by presenting a comprehensive mathematical proof using a deductive-mathematical approach that involves the Extreme Value Theorem and the Comparison Theorem. Given a continuous function and an integrable function that does not change sign on the interval , it is proven that there exists at least one point such that:
The article also provides various examples of the theorem’s application, including numerical computations using the Newton-Raphson method to determine the value of in certain cases. In addition, case studies are presented that link the theorem to modeling in probability, economics, and engineering, thereby demonstrating its relevance in data analysis and dynamic systems. The results of this study not only enrich the theoretical foundation of integral analysis but also offer practical contributions to problem solving in various disciplines
Bayesian-Negative Binomial Regression on Underreported Counts of Indonesian Female Trafficking Cases in 2023 using MCMC
Get PDFThe five-year report of the Task Force for the Prevention and Handling of Human Trafficking shows that in Indonesia from 2015 to 2019, 87.58% of human trafficking victims were women. Data of human trafficking cases often suffer from underreporting counts, where the number of reported incidents is smaller than the actual number of incidents. This study aims to estimate the actual number of cases of Indonesian female trafficking in 2023 using negative binomial regression underreported counts. Parameter estimation is conducted using a Bayesian approach through the Markov Chain Monte Carlo (MCMC) method with Gibbs sampling algorithm with a total of 5000 iterations and a burn-in period after 3000 iterations. This study utilizes secondary data sourced from Central Java Data Portal and Central Bureau of Statistics Indonesia, with the dependent variable is the reported number of Indonesian female trafficking in 2023 (Y) and three independent variables that are factors influencing female trafficking: the percentage of the poor population ( ), the open unemployment rate ( ), and the level of high school or equivalent education completion ( ). The estimated actual number of female trafficking cases in 2023 in Aceh and West Sumatra is 4 and 2 cases respectively, with the unreported number of female trafficking cases amounting to 2 cases each. The average of actual number of Indonesian female trafficking in 2023 is 9 cases, while the average of unreported number of Indonesian female trafficking in 2023 is 2 case
Forecasting Analysis of Electricity Consumption in East Kolaka and Konawe Districts Using Prophet Method
Get PDFThis study aims to determine electricity consumption forecasting in East Kolaka Regency and Konawe Regency using the Prophet method. The data used in this study are secondary data obtained from PT PLN ULP Unaaha which consists of data on the amount of monthly electricity consumption from January 2019 to November 2023. The results showed that the Prophet method obtained an error calculation value using MAPE of 1.09%. So that the Prophet method can be used to forecast electricity consumption in East Kolaka Regency and Konawe Regency