Hasil untuk "Probabilities. Mathematical statistics"

M. Malik

Faten Azeez Mustafa

In recent years, artificial intelligence (AI) has advanced quickly, equal or perhaps even outperforming human accuracy in tasks like picture recognition, reading comprehension, and text translation.  Large-scale opportunities that were not previously available are now had been created by the confluence of AI and GIS with remote sensing data processing. The motivation of current study is to incorporate deep learning models that implemented through ArcGIS Pro tools particularly convolutional neural networks (CNNs), identifying complex patterns and features in high-resolution image. An automated Deep Learning model type Mask R-CNN had applied to extract model for training objects. The overall accuracy metric improved the performance of the current work accurately with less error when calculating RMSE criteria.

Joseph Johnson Kwabina Arhinful, Emmanuel deGraft Johnson Owusu-Ansah, Burnett Tetteh Accam et al.

This work uses the Bayesian Poisson-Hidden Markov Model (BP-HMM) to develop a model that properly describes the blood type distribution among newly diagnosed COVID-19 patients. The study estimated the number of Hidden states for COVID-19 datasets from Ghana based on blood type distribution. The study's results show that the number of hidden states and rates of infection vary by blood type, four hidden states were found for the $AB^{-}$ blood group whereas all the others had five each. It was established that, the blood group O had the highest infection rate and more susceptible for an infected person deteriorated through the transition states.

T. M. Weldegerima, T. B. Gebresilassie, T. B. Gebresilassie

<p>Drought is one of the recurring natural phenomena affecting the socio-economic and environmental well-being of southern Ethiopia's society. The availability of insufficient ground-based rainfall observatory networks is limiting drought-monitoring and early-warning investigations. The main objective of this study is to analyze spatial and temporal drought characteristics using high-resolution satellite-based rainfall products for the 1991–2022 period in the Southern Nations, Nationalities, and Peoples (SNNP) region of Ethiopia. The satellite-based rainfall product used in this study was selected after the evaluation of three satellite products, namely the Africa Rainfall Climatology version 2 (ARC2), the Climate Hazards Group InfraRed Precipitation with Stations (CHIRPS), and the Tropical Applications of Meteorology using SATellite and ground-based observations (TAMSAT), against station-based rainfall for the study area space and time domains. The statistical metrics of correlation coefficient (CORR), bias (BIAS), percent bias (PBIAS), mean error (ME), mean absolute error (MAE), root mean square error (RMSE), and Nash–Sutcliffe efficiency coefficient (NSE) were used to compare and evaluate the satellite rainfall products. Accordingly, the CHIRPS shows the highest CORR of 0.96 and the highest BIAS of 1.02, which is very near to the perfect value (BIAS <span class="inline-formula">=</span> 1), followed by the TAMSAT. Hence, the CHIRPS-based satellite rainfall product was used to assess the spatio-temporal patterns of meteorological drought based on the 3-month and 12-month standardized precipitation index (SPI). The results successfully grasped the known historical and recent droughts of 2022, 2021, 2015, 2014, 2010, 2009, and 2000. A high intensity and a high severity of drought were noted in the SPI-3, while the least occurrences of extreme events were recorded in the SPI-12. Additionally, severe drought situations were detected in the drought-prone areas in the southern and southeastern parts of the SNNP region. Finally, the study concludes that, to construct grid-based drought-monitoring tools for the development of early-warning systems, the CHIRPS rainfall product can be used as an additional source of information.</p>

Vika Yugi Kurniawan, Bayu Purboutomo, Nughthoh Arfawi Kurdhi

Let  be a commutative ring, and  denote the set of all idempotent elements of . The triple idempotent graph of , denoted by , is defined as an undirected simple graph whose vertex set . Two distinct vertices u and v in  are adjacent if and only if there exists  where  and  such that , and . This definition generalizes the notion of an idempotent divisor graph by involving a triple product, which allows deeper exploration of the combinatorial behavior of idempotents in rings. In this research, we investigate the properties of the triple idempotent graph of the ring of integers modulo n, denoted by . As a results, we establish that  and , provided that the graph is connected. Furthermore,  is Hamiltonian if n is a prime and , and Eulerian if n is a prime and .

Chen Xinrong, Hongxing Liu

The paper provides a study of pseudo MV-algebras with $n$-roots. We outline their main properties and establish that the class of MV-algebras with $n$-roots forms a variety. Then, we introduce the concept of a strict $n$-root to classify the class of pseudo MV-algebras with $n$-root and demonstrate an equivalence between this variety and the class of $n$-divisible unital $\ell$-groups. Finally, we find a relationship between strongly atomless pseudo MV-algebra and strict pseudo MV-algebras. \\ \textbf{Keywords}: Pseudo MV-algebra; Square root; n-root; n-strict MV-algebra; Boolean algebra; Strongly atomless

Gilbert Alvaro Souisa, Reyner M. Leiwakabessy, Salma Damayanti et al.

Economic activity data is needed quickly to make policy decisions, but this data suffers from publication delays. Gross Domestic Product (GDP) data is released within five weeks after the end of the quarter. An effort that can be made to provide such data is through nowcasting, which is forecasting in the current period using variables that have a higher frequency. This study aims at nowcasting GDP growth. The nowcasting method used is the Dynamic Factor Model (DFM) with Two Step (TS) and Quasi Maximum Likelihood (QML) estimation. The nowcasting results show that the DFM-TS model is better than the DFM-QML because it has a larger adjusted R-squared value and has the smallest RMSE value of 1.71035 compared to the DFM-QML value, which has an RMSE value of 1.71598.

Kiswara Agung Santoso, Ade Ratna Yusnita, Agustina Pradjaningsih

Scheduling in construction projects is necessary so that the planned time to complete the project can be achieved on time. the methods used in optimizing project scheduling are the Project Evaluation Review Technique (PERT) method and the Critical Path Method (CPM) method. Bedugul  Villa is one of the projects that has been carried out with a work contract for 175 calendar days and the scheduling of which will be optimized in this study. The optimal duration for scheduling with the PERT method is to produce an optimal duration of 170 calendar days. The duration is 5 days faster than the existing schedule prepared by the project construction contractor, which is 175 calendar days. The probability of completion of the project is 87.7%. Calculations using the CPM method are 168 calendar days or 7 days earlier than the existing schedule made by the contractor.

Sarikul Islam, Nitin Gupta

An extension of Archimax copula class in more than two random variables ( Multivariate ) was introduced in (Jágr 2011) for describing dependency structures among random variables in higher dimension, and some properties of Archimax copula were explored in (Charpentier et al. 2014). In this article, some results for stochastic ordering of extreme order statistics in (Li and Fang 2015) are generalized and proved in Archimax copula. Stochastic ordering of sample extremes for PHR models is generalized and proved in Archimax copula. Examples with graphical illustrations are also presented.

C. Batanero, R. Álvarez-Arroyo

In this paper, we develop a personal synthesis of the most outstanding research on the teaching and learning of probability in the past years. We conducted a systematic search to examine publications on this topic in mathematics education, statistics education, education, and psychology journals. This exploration was complemented by additional studies published in conference proceedings or books. We classified these papers to highlight the main recent research tendencies in the field, according to the theme studied and considering the research objectives. Epistemological analyses suggest that informal inference based on simulation diminishes the topic abstraction but reduces probability to its frequentist view. Topics receiving particular attention include children’s probabilistic knowledge, the effect of visualizations on solving conditional probability problems, teachers’ education and probability modelling. In the final section, we recommend relevant points in which more investigation is needed to complete our knowledge about teaching and learning. In particular, we miss research on teachers’ mathematical knowledge of many probability concepts and on their didactic knowledge.

Sanjay Ghevariya, CHETANBHAI PATEL

A famous Black-Scholes differential equation is used for pricing options in financial world which represents financial derivatives more significantly. Option is one of the crucial financial derivatives. Sawangtong P., Trachoo K., Sawangtong W. and Wiwattanapataphee B. obtained analytical solution of Black-Scholes equation with two assets in the Liouville-Caputo time-fractional derivative sense using Laplace homotopy perturbation method (LHPM). The aim of this paper is to derive solution of Liouville-Caputo time-fractional Black-Scholes equation with n assets using LHPM. Numerical results shows that our approach gives very accurate results and our formulas are quite close to the plain vanilla options.

Ginger Egberts, Ginger Egberts, Fred Vermolen et al.

Severe burn injuries often lead to skin contraction, leading to stresses in and around the damaged skin region. If this contraction leads to impaired joint mobility, one speaks of contracture. To optimize treatment, a mathematical model, that is based on finite element methods, is developed. Since the finite element-based simulation of skin contraction can be expensive from a computational point of view, we use machine learning to replace these simulations such that we have a cheap alternative. The current study deals with a feed-forward neural network that we trained with 2D finite element simulations based on morphoelasticity. We focus on the evolution of the scar shape, wound area, and total strain energy, a measure of discomfort, over time. The results show average goodness of fit (R2) of 0.9979 and a tremendous speedup of 1815000X. Further, we illustrate the applicability of the neural network in an online medical app that takes the patient's age into account.

K.A. Bekmaganbetov, G.A. Chechkin, V.V. Chepyzhov et al.

In this paper the Ginzburg-Landau equation is considered in locally periodic porous medium, with rapidly oscillating terms in the equation and boundary conditions. It is proved that the trajectory attractors of this equation converge in a weak sense to the trajectory attractors of the limit Ginzburg-Landau equation with an additional potential term. For this aim we use an approach from the papers and monographs of V.V. Chepyzhov and M.I. Vishik concerning trajectory attractors of evolution equations. Also we apply homogenization methods appeared at the end of the XX-th century. First, we apply the asymptotic methods for formal construction of asymptotics, then, we verify the leading terms of asymptotic series by means of the methods of functional analysis and integral estimates. Defining the appropriate axillary functional spaces with weak topology, we derive the limit (homogenized) equation and prove the existence of trajectory attractors for this equation. Then we formulate the main theorem and prove it with the help of axillary lemmas.

solmaz taheri, Mohamad Esmaeil Akbari, hossein bonakchi et al.

Introduction: Breast cancer in men is a rare disease that has been increasing in recent decades. Identifying factors influencing the survival rate of these patients is particularly important considering the small sample size. The aim of this study was to present the results of the conventional Cox- LASSO method and compare it with the newer refined generalized log-rank (RGLR) method for analyzing survival data with a small sample size. Methods: Available information related to men with breast cancer referred to 3 treatment centers in the country (Iran) between 2012 and 2020 were reviewed. Cox-LASSO and RGLR models were fitted on the data. The analyzes were done using R.4.1.2 software and the significance level of 0.05 was considered. Results: About 60% of the conflicts are reported on the left side. About 53% of men have been diagnosed at a low stage. The tumor size of 75% of the patients was between 2 and 4.3. Most patients have received modified radical mastectomy (MRM) treatment and adjuvant radiotherapy. 80% of patients had received chemotherapy and most had received anthracycline-taxane base. According to Akaike's criterion, RGLR model (AIC=289.32) was better than Cox-LASSO (AIC=314.76) model. Results of RGLR model indicated that, age (p-value= 0.038, HR >50 vs <50 = 6.75, 95% CI: 2.70–17.30), left laterality (p-value = 0.019, HR left vs right = 3.45, 95% CI: 1.48–8.02), larger tumor size (p-value=0.033, HR T2 vs T1 = 3.70, 95% CI: 2.92–6.68; HR T3 vs T1 = 4.34, 95% CI: 3.17–5.95), higher tumor grades (p-value<0.001, HR grade 2 or 3 vs grade1 = 8.67, 95% CI: 5.10–14.71), are influential factors decreasing male breast cancer patient’s survival. Conclusion: Although the results of the two existing models in the field of small sample size survival analysis (Cox-LASSO and RGLR) are close to each other, the RGLR model has performed better than the Cox-LASSO. With smaller AIC and SE of parameter estimation, RGLR model was choose compared to Cox-LASSO model.

R S Rasin, S M Sunoj, Rakesh Poduval

The notion of ageing plays an important role in reliability and survival analysis as it is an inherent property of all systems and products. Jiang, Ji, and Xiao (2003) proposed a new quantitative measure, known as ageing intensity (AI) function, an alternative measure to study the ageing pattern of probability models. In this paper, we propose a nonparametric estimator for ageing intensity function. Asymptotic properties of the estimator are established under suitable regularity conditions. A set of simulation studies are carried out based on various probability models to examine the performance of estimator and to establish its efficiency over the classical estimator. The usefulness of the estimator is also examined through a real data set.

Sidy Danioko, Jianwei Zheng, Kyle Anderson et al.

The classical Box-Pierce and Ljung-Box tests for auto-correlation of residuals possess severe deviations from nominal type I error rates. Previous studies have attempted to address this issue by either revising existing tests or designing new techniques. The Adjusted Box-Pierce achieves the best results with respect to attaining type I error rates closer to nominal values. This research paper proposes a further correction to the adjusted Box-Pierce test that possesses near perfect type I error rates. The approach is based on an inflation of the rejection region for all sample sizes and lags calculated via a linear model applied to simulated data that encompasses a large range of data scenarios. Our results show that the new approach possesses the best type I error rates of all goodness-of-fit time series statistics.

Federico Bergamin, Pierre-Alexandre Mattei, Jakob D. Havtorn et al.

We present simple methods for out-of-distribution detection using a trained generative model. These techniques, based on classical statistical tests, are model-agnostic in the sense that they can be applied to any differentiable generative model. The idea is to combine a classical parametric test (Rao's score test) with the recently introduced typicality test. These two test statistics are both theoretically well-founded and exploit different sources of information based on the likelihood for the typicality test and its gradient for the score test. We show that combining them using Fisher's method overall leads to a more accurate out-of-distribution test. We also discuss the benefits of casting out-of-distribution detection as a statistical testing problem, noting in particular that false positive rate control can be valuable for practical out-of-distribution detection. Despite their simplicity and generality, these methods can be competitive with model-specific out-of-distribution detection algorithms without any assumptions on the out-distribution.

T. Fritz, Tomáš Gonda, Paolo Perrone et al.

Markov categories are a recent categorical approach to the mathematical foundations of probability and statistics. Here, this approach is advanced by stating and proving equivalent conditions for second-order stochastic dominance, a widely used way of comparing probability distributions is by their spread. Furthermore, we lay foundation for the theory of comparing statistical experiments within Markov categories by stating and proving the classical Blackwell-Sherman-Stein Theorem. Our version not only offers new insight into the proof, but its abstract nature also makes the result more general, automatically specializing to the standard Blackwell-Sherman-Stein Theorem in measure-theoretic probability as well as a Bayesian version that involves prior-dependent garbling. Along the way, we define and characterize representable Markov categories, ones that can describe spaces of distributions. We do so by exploring the relation between Markov categories and Kleisli categories of probability monads.

Zubair Ahmad, M. Elgarhy, G. Hamedani et al.

A new family of distributions called the odd generalized N-H is introduced and studied. Four new special models are presented. Some mathematical properties of the odd generalized N-H family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics and Rényi entropy are investigated. Characterizations based on the truncated moments, hazard function and conditional expectations are presented for the generated family. Parameter estimates of the family are obtained based on maximum likelihood procedure. Two real data sets are employed to show the usefulness of the new family.

Hazem Al-Mofleh, M. Elgarhy, A. Afify et al.