Fardinah Fardinah, Hikmah Hikmah, Rahmah Abubakar
et al.
This study discusses the intervention of cannibalism and disease spread with Holling Type II response function in the predator-prey model. It is assumed that disease infection is limited to the prey population and cannot be cured so that in this model there are three subpopulations namely susceptible prey, infected prey and predators. In addition, there is cannibalism in the predator population. The objectives of this study include constructing a predator-prey model with cannibalism intervention and disease infection in prey using Holling Type II response function, identifying the stability of the equilibrium point of the model and interpreting the model based on simulation results. Analysis of the stability of the equilibrium point is carried out with a linearization approach and the Routh-Hurwitz criterion was used to determine equilibrium stability. Based on the stability analysis, 5 (five) equilibrium points are obtained, namely population extinction, susceptible prey exists, predator extinction, infected prey extinction and population exists where the population extinction equilibrium point is unstable and the other equilibrium points are stable with the certain conditions. From the simulation, it is obtained that the numerical results are in accordance with the analytical results of the stability analysis of the equilibrium point of the model and for infinite time, there will be no population extinction while the state of susceptible prey exists, predator extinction, infected prey extinction and population exists can occur if the stability conditions are met. Based on the numerical simulations, it was found that changes in the parameter values of the rate of change of susceptible prey to infected prey and the coefficient of predator cannibalism in day-1 can cause changes in the type of stability of the equilibrium point. Thus, rate of change susceptible prey to infected prey and the coefficient of predator cannibalism affects the population of prey and predator.
On a single machine, each of n jobs must be processed continuously. At time zero, every job is ready for processing. The tasks to process a sequence that minimizes the total sum of competition times plus the sum of tardiness . This bi-criteria problem is NP-hard because of the second one. We provide a theorem that demonstrates a relationship between the optimal solution, lower bounds, and the number of efficient solutions. The case is that the theorem works for NP-hard problems, whereas in previous works the focus was on P-hard problems. The theorem limits the lower bound's range, which is crucial for determining the best answer. Additionally, the theorem allows for discovering new lower bounds by opening algebraic procedures and concepts.
Aulia Rahman Al Madani, Sandrina Najwa, Budi Nurani Ruchjana
Indonesia's economic growth has undergone significant fluctuations in recent years, driven by global shocks such as the 2020 COVID-19 pandemic, the 2013 taper tantrum, and the 2022 global energy crisis. These events underscore the urgent need for more accurate and robust forecasting models to support economic stability and policymaking. This study applies the Principal Component Analysis-Vector Autoregressive Integrated (PCA-VARI) model to forecast economic growth in Indonesia. PCA reduces seven economic variables into two principal components for ten years (2012-2022). The results show that the first component (PC1) shows the highest correlation with the variables of Money Supply, BI Rate, and Foreign Exchange Reserves, which reflect monetary policy and financial stability. Meanwhile, the second component (PC2) is highly correlated to the GDP Index, Exchange Rate, and Inflation variables, which reflect macroeconomic conditions. VARI, as a non-stationary multivariate time series model, is used to model the relationship between these components, with the third-order lag selected as the optimal lag based on the Akaike Information Criterion (AIC), Hannan-Quinn Criterion (HQ), and Final Prediction Error (FPE) values. The results show that the PCA-VARI(3) model is able to provide highly accurate forecasting with a MAPE of 1.21% for PC1 and 1.34% for PC2, and has met all the necessary model assumptions.
Bias in causal comparisons has a correspondence with distributional imbalance of covariates between treatment groups. Weighting strategies such as inverse propensity score weighting attempt to mitigate bias by either modeling the treatment assignment mechanism or balancing specified covariate moments. This article introduces a new weighting method, called energy balancing, which instead aims to balance weighted covariate distributions. By directly targeting distributional imbalance, the proposed weighting strategy can be flexibly utilized in a wide variety of causal analyses without the need for careful model or moment specification. Our energy balancing weights (EBW) approach has several advantages over existing weighting techniques. First, it offers a model-free and robust approach for obtaining covariate balance that does not require tuning parameters, obviating the need for modeling decisions of secondary nature to the scientific question at hand. Second, since this approach is based on a genuine measure of distributional balance, it provides a means for assessing the balance induced by a given set of weights for a given dataset. We demonstrate the effectiveness of this EBW approach in a suite of simulation experiments, and in studies on the safety of right heart catheterization and on three additional studies using electronic health record data.
Winita Sulandari, Yudho Yudhanto, Riskhia Hapsari
et al.
Prophet is one of the machine learning approximation methods that accommodate trends, seasonality, and holiday impacts in time series data. Generally, the performance of machine learning models can be improved by implementing hyperparameter tuning. This study investigates whether hyperparameter tuning can improve the model's performance. To show its effectiveness, the Prophet model constructed by parameter tuning is compared to the one with fixed parameter values (namely the default model) for both the original series and the Box-Cox transformed series in terms of mean absolute percentage error (MAPE). Based on the experimental results of the twenty-four daily electricity load time series in American Electric Power (AEP). This shows that parameter tuning successfully reduces the MAPE of the default model in the range of about 3-8% for training data. However, there is no guarantee for testing data. Although, in some cases, parameter tuning can reduce the MAPE value of the default model by up to 38%, in other cases, it actually increases the MAPE of the default model by almost 15%. The experiments on testing data also show that models built from transformed data do not necessarily produce more accurate forecast values than those built from the original data.
Jonathan Prasetyo Johan, Felivia Kusnadi, Benny Yong
Reserves are one of the most crucial components for an insurance company to make sure it has enough money to pay off all the incurred claims. The presence of outliers in the incurred claims data harbors risk on inaccurately predicting reserves to cover claim amounts, usually achieved by the standard chain ladder reserving method. To remedy the effect of the outliers, the robust chain ladder reserving method is used by setting the median value to predict estimated reserve. On this research, we utilized both methods on various datasets. The purpose of this paper is to determine the best method that can be utilized by insurance company in various scenario to obtain the most optimized reserved estimate that can minimize the risk of being unable to pay the insurance claim or even the risk of over allocating reserves that could pose profitability issue. The primary data used are the Australian domestic motor insurance claims from 2012 to 2017, obtained from Australian Prudential Regulation Authority (APRA). The dataset is then manipulated to have outliers. After calculating the estimation, the result is compared to assess the strength of the methods using Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) calculation. In conclusion, we found that the robust chain ladder reserving method works better in an outlying dataset. We also identify cases in which robust chain ladder are not appropriately used.
Background: The multidimensional item response theory (MIRT) model provides an ideal foundation for assessing the psychological properties of a questionnaire designed with multidimensional structure. This study aimed to present the first use of MIRT models to investigate the psychometric properties of general health questionnaire (GHQ-12) in parents of school-aged children.
Methods: A total of 1104 parents of school children-aged completed the Persian version of GHQ-12 questionnaire. The unidimensional IRT model and MIRT models with two and three factors were applied to model the observed scores for each GHQ-12 item as a function of the subject’s latent traits while taking the correlation among dimensions of the questionnaire into account. Goodness of fit indices were reported for the three models, and the fits of items were assessed for the best model. Individual items were described in detail through item characteristic curves, and the amount of information carried by different items was presented using information curves.
Results: The MIRT analysis with three factors corresponding with anxiety depression, social dysfunction and loss of confidence provided the best account of the GHQ-12 data. The model showed that all items were fitted adequately. Items varied in their discrimination ranged from 0.94 to 2.13, 1.31 to 2.74, and 2.87 to 3.57 for social dysfunction, anxiety depression, and loss of confidence, respectively. Moreover, items 8 and 2 provided the least information in social dysfunction and anxiety depression dimensions, respectively. Items in the loss of confidence dimension carried the most information among all items of the GHQ-12.
Conclusions: The developed framework for evaluating the psychometric properties of GHQ-12 can be a suitable alternative to traditional approaches as well as unidimensional IRT models, the use of which has been restricted due to the multidimensional structure of the questionnaire.
In this paper, a numerical method based on a finite difference scheme is proposed for solving the time-fractional diffusion equation (TFDE). The TFDE is obtained from the standard diffusion equation by replacing the first-order time derivative with Caputo fractional derivative. At first, we introduce a time discrete scheme. Then, we prove the proposed method is unconditionally stable and the approximate solution converges to the exact solution with order O(Δt2−α)O(Δt2−α), where ΔtΔt is the time step size and αα is the order of Caputo derivative. Finally, some examples are presented to verify the order of convergence and show the application of the present method.
Probabilities. Mathematical statistics, Instruments and machines
We consider the differential equation f’’’ +ff’’ +β(f’^2 – 1) = 0, with β > 0. In order to prove the existence of solutions satisfying the boundary conditions f (0) = a ≥ 0, f’(0) = b ≥ 0 and f’(+∞) = −1 or 1 for 0 < β ≤ 1/2 . We use shooting technique and consider the initial conditions f (0) = a, f’(0) = b and f‘’(0) = c. We prove that there exists an infinitely many solutions such that f’(+∞) = 1.
In this paper some generalized exponential-type chain estimators have been proposed for the finite population mean in the presence of nonresponse under stratified two-phase sampling when mean of another auxiliary variable is readily available. The expressions for the bias and mean square error of proposed estimators have been derived. The comparisons for proposed estimators have been made in theory with Hansen-Hurwitz’s, J. Am. Stat. Assoc. 41 (1946), 517–529, and Tabasum and Khan’s, J. Indian Soc. Agric. Stat. 58 (2004), 300–306, two-phase ratio and product estimators modified to the stratified sampling. An empirical study has also been carried out to demonstrate the performances of the estimators.
Air Quality Modeling gained great importance in atmospheric pollution because of its negative effects on the environment and human health. In our study, the relationship between (Particulate Matter PM<sub>10</sub>) and other nine variables over three years is studied to applied the multiple linear regression models. The seasonal influences for seasonally periods lead to difficult analyzing and forecasting. Therefore, Time-stratified (TS) approach is used into seasonally. The multiple linear regression
(MLR) model is the most common for studying like this number of variables. Genetic algorithm (GA) as well as their hybrid method such as MLR–GA, is proposed to reduce the number of studied variables. Reducing the number of variables may also lead to more accurate results. The genetic algorithm has improved the performance of MLR method separately. GA also improved MLR performance by using hybrid method MLR-GA.
Lisa Bloomer Green, Nancy McCormick, Scott McDaniel
et al.
A course community (CC) was formed to facilitate the implementation of active-learning materials in the Introductory Statistics course at a large southeastern U.S. university. Instructors met every two weeks for the semester before and the semester of the implementation. The CC helped instructors improve their content knowledge and pedagogical skills. Results show improvement in teacher attitudes and in student scores.
Special aspects of education, Probabilities. Mathematical statistics
An existing one-parameter probability distribution can be very well generalized by adding an extra parameter in it and, in turn, the two-parameter family of distributions, thus obtained, provides added flexibility in modeling real life data. In this article, we propose and study a two-parameter generalization of xgamma distribution [1] and utilize it in modeling time-to-event data sets. Along with the different structural and distributional properties of the proposed two-parameter xgamma distribution, we concentrate in studying useful survival and reliability properties, such as hazard rate, reversed hazard rate, stress-strength reliability etc. Two methods of estimation, viz. maximum likelihood and method of moments, are been suggested for estimating unknown parameters. Distributions of order statistics, stochastic order relationships are investigated for the proposed model. A Monte-Carlo simulation study is carried out to observe the trends in estimation process. Two real life time-to-event data sets are analyzed and the proposed model is compared with some other two-parameter lifetime models in the literature
The periodic boundary value problem for the system of hyperbolic equations with delayed argument is considered. By method of introduction a new functions the investigated problem reduce to an equivalent problem, consisting the family of periodic boundary value problem for a system of differential equations with delayed argument and integral relations. Relationship of periodic boundary value problem for the system of hyperbolic equations with delayed argument with the family of periodic boundary value problems for the system of ordinary differential equations with delayed argument is established. Algorithms for finding solutions of the equivalent problem are constructed and their convergence is proved. Sufficient and necessary conditions of well - posedness of periodic boundary value problem for the system of hyperbolic equations with delayed argument are obtained.
Keretapi Tanah Melayu Berhad (KTMB) is the main rail operator in Peninsular Malaysia. KTMB provides cargo services which are safe, efficient and trustworthy. KTMB also has services that are connected to the port and inland port in Peninsular Malaysia. However, they remove suffered three major derailments in 2017. On November 23, a cargo train had an accident when 12 cargo trains traveling southward slipped between National Bank Station and Kuala Lumpur Station due to heavy weight and oversized loads carried by the cargo train. This study is conducted to predict the amount of carried weight of cargo by KTMB using Artificial Neural Network model. Datasets used in this study was taken from Department of Statistics Malaysia Official Portal from year 2001 to 2016. There are three algorithms chosen in this study which are Conjugate Gradient Descent (CGD), Quasi-Newton (QN) and Lavenberg-Marquardt (LM) algorithm. The best algorithm is selected to predict the amount of carried weight by comparing the value of error measures of the three algorithms which are Root Mean Squared Error (RMSE) and Mean Absolute Percentage Error (MAPE). Therefore, CGD is the best algorithm that produces smallest error of RMSE and MAPE. By using CGD algorithm, the results show the forecast value of carried weight for five years ahead which is from year 2017 until 2021 is decrease.
SummaryThis paper presents a comparison of three approaches to the teaching of probability to demonstrate how the truth table of elementary mathematical logic can be used to teach the calculations of conditional probabilities. Students are typically introduced to the topic of conditional probabilities—especially the ones that involve Bayes' rule—with the help of such traditional approaches as formula use or conversion to natural frequencies. The truth table approach is an alternative method for explaining the concept and calculation procedure of conditional probability and Bayes' rule.