Hasil untuk "Probabilities. Mathematical statistics"

Sudianto Manullang, Marlina Setia Sinaga, Pardomuan N. J. M. Sinambela et al.

This study aims to analyze the survival of CHD patients during hospitalization using survival analysis methods. The Kaplan–Meier method was applied to estimate survival probabilities, and group differences were tested using the log-rank test. Furthermore, the Cox proportional hazards model with the Breslow approach was used to assess the effect of clinical factors on survival, with assumptions verified using Schoenfeld residuals. By integrating nonparametric and semiparametric survival methods, this study provides a more comprehensive assessment of CHD patient survival compared with previous studies that relied on a single analytical approach. Data were collected retrospectively from 150 inpatients at Haji General Hospital, Medan, between 2021 and 2022, with 45 cases identified as censored. The Kaplan–Meier analysis revealed a progressive decline in survival probability during hospitalization, with the survival rate decreasing from 69.3% on the first day to 5.3% by day 40. The log-rank test results indicated that only hypertension had a statistically significant effect on patient survival (p < 0.001), while age, gender, and cholesterol status were not significant (p > 0.05). The Cox regression analysis confirmed these findings, showing that CHD patients with hypertension had more than three times higher risk of death (HR = 3.13; 95% CI: 2.06–4.78) compared to those without hypertension. These findings highlight hypertension as the most dominant risk factor reducing survival among CHD patients during hospitalization. This supports prioritizing early detection and intensive monitoring for hypertensive CHD patients to improve in-hospital clinical outcomes. However, this study has limitations due to its single-center retrospective design and the use of only four variables, leaving out other clinical factors that may influence survival outcomes.

Jasten Keneth De las Nadas Treceñe, Reynalyn O. Barbosa

Efficient energy management has become a critical concern across all sectors due to rising costs and sustainability imperatives. In universities, electricity expenditure represents a substantial share of operational budgets, prompting the need for accurate forecasting models to support financial planning and sustainability initiatives. This study proposed a hybrid forecasting model integrating Simple Exponential Smoothing (SES) and Long Short-Term Memory (LSTM) networks to predict monthly electricity expenditure in a university setting. SES acts as a linear smoothing operator, emphasizing recent trends, while LSTM serves as a nonlinear sequence learner capable of modeling long-term dependencies. The hybrid formulation embeds SES forecasts as auxiliary input features to LSTM, thereby balancing interpretability with predictive power. A dataset of 60 monthly electricity expenditure observations (2019–2023) from Eastern Visayas State University–Tanauan Campus was analyzed. The proposed model was compared against classical (SES, ARIMA) and deep learning (LSTM, FB Prophet) approaches. Results show that the hybrid model achieved superior performance (RMSE = 33760.68, MAPE = 32.32%, MAE = 24580.12), with statistical validation through the Diebold-Mariano test, which confirmed significant improvements. Residual and uncertainty analyses demonstrated the model's robustness and practical applicability. The proposed model positioned it as a valuable decision-support tool for energy cost forecasting and risk-aware planning in universities.

John Wilson

Airlines profitability increasingly depends on the sale of ancillary items such as seat selection, baggage fees, etc. The modeling of ancillary items is becoming more important in the analytics literature. Much of the modeling is stylized and not immediately applicable. This paper contains a review of the approaches and modeling assumptions made in the literature. The focus is on the assumptions made so that models may be evaluated for how effective they are for applications and to highlight gaps in the literature.

Barb Bennie, Richard A. Erickson

AbstractEffective undergraduate statistical education requires training using real-world data. Textbook datasets seldom match the complexities and messiness of real-world data and finding these datasets can be challenging for educators. Consulting and industrial datasets often have nondisclosure agreements. Academic datasets often require subject area expertise beyond those of a general education or lack connections to real-world applications. Many governments, including the United States, now require the release of data from projects they directly complete or fund though grants and contracts. We show how statistical educators may find datasets and incorporate them into courses. Specifically, we use two examples from the U.S. Geological Survey (USGS) and one example from the ecology literature. We demonstrate the use of these datasets in an upper-level analysis of variance (ANOVA) class. In addition to describing how we found the datasets, we describe how to include them into course work and the course’s student assessments. We have used these datasets over multiple semesters and included student feedback from these courses. Although our examples focus on an ANOVA class, the general methods for finding data shared here could be used for statistical classes ranging from high school to graduate education. Supplementary materials for this article are available online.

Strieder David, Drton Mathias

Inferring the effect of interventions within complex systems is a fundamental problem of statistics. A widely studied approach uses structural causal models that postulate noisy functional relations among a set of interacting variables. The underlying causal structure is then naturally represented by a directed graph whose edges indicate direct causal dependencies. In a recent line of work, additional assumptions on the causal models have been shown to render this causal graph identifiable from observational data alone. One example is the assumption of linear causal relations with equal error variances that we will take up in this work. When the graph structure is known, classical methods may be used for calculating estimates and confidence intervals for causal-effects. However, in many applications, expert knowledge that provides an a priori valid causal structure is not available. Lacking alternatives, a commonly used two-step approach first learns a graph and then treats the graph as known in inference. This, however, yields confidence intervals that are overly optimistic and fail to account for the data-driven model choice. We argue that to draw reliable conclusions, it is necessary to incorporate the remaining uncertainty about the underlying causal structure in confidence statements about causal-effects. To address this issue, we present a framework based on test inversion that allows us to give confidence regions for total causal-effects that capture both sources of uncertainty: causal structure and numerical size of non-zero effects.

Rojhun O. Macalinao, Jcob C. Malaguit, Destiny S. Lutero

Onsite classes in the Philippines have been prohibited since March 2020 due to the SARS-CoV-2 which causes the COVID-19. This forced millions of learners to adapt with new modes of instruction that may not be optimal for their learning. In this study, we implemented an agent-based model in Netlogo that followed common classroom layouts to assess the effects of human interactions to virus transmission. Results show that the highest value of cumulative proportion of infected individuals inside the classroom (CPI) is achieved when the total allowable seating capacity in the classroom is increased from 25 to 50%. Also, varying transmission rates between 5 and 20% does not pose any significant effect on CPI. Furthermore, in three of the four seating arrangements, allowing in-class mobility and class rotations can pose significant increases in CPI averaging from 40 to 70%. Results also showed that factors including maximum number of students and number of initially infected individuals, significantly affect the likelihood of infection apart from the seating arrangement itself. To minimize the risk of transmission inside the classroom setup considered, it is vital to control these factors by adhering to mitigation efforts such as increased testing and symptoms checking, limiting the maximum number of students, and redefining breaks and class rotations.

Darlena Darlena, Ari Suparwanto

If the characteristic polynomial of a linear operator  is completely factored in scalar field of  then Jordan canonical form  of  can be converted to its rational canonical form  of , and vice versa. If the characteristic polynomial of linear operator  is not completely factored in the scalar field of  ,then the rational canonical form  of  can still be obtained but not its Jordan canonical form matrix . In this case, the rational canonical form  of  can be converted to its Jordan canonical form by extending the scalar field of  to Splitting Field of minimal polynomial   of , thus forming the Jordan canonical form of  over Splitting Field of  . Conversely, converting the Jordan canonical form  of  over Splitting Field of  to its rational canonical form uses symmetrization on the Jordan decomposition basis of  so as to form a cyclic decomposition basis of  which is then used to form the rational canonical matrix of

Mahmoud R. Mahmoud, Hiba Z. Muhammed, Ahmed R. El-Saeed et al.

In this paper, we consider generalized inverted exponential distribution which is capable of modeling various shapes of failure rates and aging processes. Based on progressive Type-I censored data, we consider the problem of estimation of parameters under classical and Bayesian approaches. In this regard, we obtain maximum likelihood estimates and Bayes estimates under squared error loss function. We also compute a 95% asymptotic confidence interval, bootstrap confidence intervals and highest posterior density (HPD) credible interval estimates. Finally, we analyze a real data set and conduct a Monte Carlo simulation study to compare the performance of the various proposed estimators.

Diana Sirmayunie Mohd Nasir, Nurul Hahani Che Baharom, Nor Hayati Shafii et al.

A shift work schedule is extremely important to obtain the optimum result of work allocation since it involves 24 hours of continuous services. Every nurse could not avoid shift work schedule since their services are very important towards the patients in the hospital. The major objective of the study is to propose a cyclical nurse scheduling in the Coronary Care Unit (CCU) at Shah Alam hospital using Goal Programming. It is to help the head nurse to spend less effort on building new schedules periodically and increase the satisfaction among nurses by providing fairness towards their schedules. There were nine hard constraints and three soft constraints for the nurse scheduling model. The results presented the optimal solution where all goals were achieved thus, it provided a fair schedule for 15 nurses in 15 days. Then, the schedule pattern was rotated among nurses based on the 15 schedules set in 225 days. The first schedule set will be used by the nurse for the first 15 days, then will be continuously rotated for another 15 days until all the nurses reached and experienced every 15 sets of the schedule. The schedule was generated using LINGO software which it took a short time to solve the problem.

M.V. Babii, V.O. Nastasenko, V.O. Protsenko et al.

In the article mathematical dependencies to determine the gripping force of the cutting plate in the socket of assembled cutoff tools with the lateral installation of multifaceted unresharpenable plates (MUP) are proposed for the first time, which makes it impossible to move the plate in any direction while the cutting forces acting on it. Moreover, the expressions are obtained to determine the minimum height of the intersection of the cutoff tool socket head, which is important at the stage of creating a methodology for designing this type of tool.

Mutti-Ur Rehman, M. Fazeel Anwar

In this article we present the computations of lower bounds of well-known mathematical quantity in control theory known as structured singular value for a family of structured matrices obtained for a DC Motor, that is an electrical machine. The comparison of lower bounds with the well-known MATLAB function mussv is studied. The structured singular values provide an important tool to synthesize robustness as well as analyze performance and stability of feedback systems.

Özkan Öcalan, Nurten Kilic, Sermin Sahin et al.

<p>Consider the first-order nonlinear retarded differential equation</p> <p>$$</p> <p>x^{\prime }(t)+p(t)f\left( x\left( \tau (t)\right) \right) =0, t\geq t_{0}</p> <p>$$</p> where $p(t)$ and $\tau (t)$ are function of positive real numbers such that $%\tau (t)\leq t$ for$\ t\geq t_{0},\ $and$\ \lim_{t\rightarrow \infty }\tau(t)=\infty $. Under the assumption that the retarded argument is non-monotone, new oscillation results are given. An example illustrating the result is also given.<br />

Lyn D. English, J. Watson

Mehmet Zeki Sarikaya, Fuat Usta

In this paper the more general comparison theorems for conformable fractional differential equations is proposed and tested. Thus we prove some inequalities for conformable integrals by using the generalization of Sturm's separation and Sturm's comparison theorems. The results presented here would provide generalizations of those given in earlier works. The numerical example is also presented to verify the proposed theorem.

Ferdinando Casolaro, Luca Cirillo, Raffaele Prosperi

This paper deals with groups of transformations with finite number of isometrics and, therefore, appears as the completion of previous and published works (Casolaro, F. L. Cirillo and R. Prosperi 2015) related only to endless groups of transformations with isometrics. In particular isometries of the tetrahedron and the cube are presented which turn these figures in itself.

Pavel Tuček, Jaroslav Marek

-

J. Benedetto, Michael Frazier, B. Torrésani

R. Kruse, E. Schwecke, Jochen Heinsohn

Yang Chen, M. Mckay

J. Tropp