Hasil untuk "Probabilities. Mathematical statistics"

K.T. Karimov, M.R. Murodova

The paper investigates a Dirichlet-type boundary value problem for a three-dimensional elliptic equation with three singular coefficients in the first octant. The uniqueness of the solution within the class of regular solutions is established using the energy integral method. To prove the existence of a solution, the Hankel integral transform method is employed. The use of the Hankel transform is particularly appropriate when the variables in the equation range from zero to infinity. This transform is an effective method for obtaining solutions to such problems. In three-dimensional space, to derive the image equation, the Hankel integral transform is applied to the original equation with respect to the variables x and y. As a result, a boundary value problem for an ordinary differential equation in the variable z arises. By solving this problem, a solution to the original boundary value problem is constructed in the form of a double improper integral involving Bessel functions of the first kind and Macdonald functions. To justify the uniform convergence of the improper integrals, asymptotic estimates of the Bessel functions of the first kind and Macdonald functions are utilized. Based on these estimates, bounds for the integrands are obtained, which ensure the convergence of the resulting double improper integral, that is, the solution to the original boundary value problem and its derivatives up to second order, inclusively, as well as the theorem of existence within the class of regular solutions.

Miftahurrahman Miftahurrahman, I Gede Adhitya Wisnu Wardhana, Nur Idayu Alimon et al.

This paper investigates the Degree Square Sum Energy , Degree Exponent Energy , and Degree Exponent Sum Energy  of the coprime graph on generalized quaternion group ​. This research is quantitative study using previous study as the literature review to construct the new theorem. These energy methods provide new insights into the spectral properties of graphs by their vertex degree distributions into eigenvalue computations. Using spectral graph theory, the general formulas for the , , and  of  ​ are formulated for  for every positive integer . Furthermore, we explore the implications of these methods in understanding the algebraic and spectral characteristics of  ​. Numerical results are presented for specific cases to validate the previous theorem. This study contributes to the broader analysis of graph energies, offering a framework for studying other algebraic structures.

G.F. Azhmoldaev, K.A. Bekmaganbetov, G.A. Chechkin et al.

We consider the reaction–diffusion system of equations with rapidly oscillating terms in the equation and in boundary conditions in a domain with locally periodic oscillating boundary. In the subcritical case (the Fourier boundary condition is changed to the Neumann boundary condition in the limit) we proved that the trajectory attractors of this system converge in a weak sense to the trajectory attractors of the limit (homogenized) reaction–diffusion systems in domain independent of the small parameter, characterizing the oscillation rate. To obtain the results we use the approach of homogenization theory, asymptotic analysis and methods of the theory concerning trajectory attractors of evolution equations. Defining the appropriate functional and topological spaces with weak topology, we prove the existence of trajectory attractors and global attractors for these systems. Then we formulate the main Theorem and prove it with the help of auxiliary Lemmata. Applying the homogenization method and asymptotic analysis we derive the homogenized (limit) system of equations, prove the existence of trajectory attractors and global attractors and show the convergence of trajectory and global attractors.

Suleman Nasiru, Christophe Chesneau, Abdul Ghaniyyu Abubakari et al.

The use of distributions to model and quantify risk is essential in risk assessment and management. In this study, the generalized unit half-logistic geometric (GUHLG) distribution is developed to model bounded insurance data on the unit interval. The corresponding probability density function plots indicate that the related distribution can handle data that exhibit left-skewed, right-skewed, symmetric, reversed-J, and bathtub shapes. The hazard rate function also suggests that the distribution can be applied to analyze data with bathtubs, N-shapes, and increasing failure rates. Subsequently, the inferential aspects of the proposed model are investigated. In particular, Monte Carlo simulation exercises are carried out to examine the performance of the estimation method by using an algorithm to generate random observations from the quantile function. The results of the simulation suggest that the considered estimation method is efficient. The univariate application of the distribution and the multivariate application of the associated regression using risk survey data reveal that the model provides a better fit than the other existing distributions and regression models. Under the multivariate application, we estimate the parameters of the regression model using both maximum likelihood and Bayesian estimations. The estimates of the parameters for the two methods are very close. Diagnostic plots of the Bayesian method using the trace, ergodic, and autocorrelation plots reveal that the chains converge to a stationary distribution.

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Mochamad Azkal Azkiya Aziz, Shahrinaz Ismail, Noormadinah Allias

Conventional-manual type of attendance systems can be very time-consuming to some extent, particularly for a significant number. The existence of face recognition technology can solve the inefficiency and ineffectiveness of conventional and manual attendance systems. Among many approaches to implement face recognition, this research focuses on using deep learning approaches as it has been proven to give promising results. There are various algorithms for face recognition, such as Local Binary Pattern Histogram (LBPH), Local Binary Pattern Network (LBPn), Haar Cascade, and Convolutional Neural Network. The use of deep learning can reach 98 percent accuracy. However, it is necessary to conduct further research on its implementation on the real system in order to evaluate the efficiency of the system.  An interview was conducted with an expert in the field, to understand the concept, trend, and use of deep learning in face recognition, as well as to determine the suitable algorithm for the attendance system.  This paper presents the results from this interview, which provide an insight based on real practices.

Mohammed EL HOUCH

ملخص: تهدف هذه الدراسة إلى رصد مظاهر العنف والعدوان في الفضاء المدرسي من ناحيتين: من الناحية الموضوعاتية عبر دراسة تيمة الكتابة على الجدران مسترشدين بمنظور التحليل النفسي لجماعة القسم بما يوفره من أدوات ومفاهيم لرصد الظواهر الواعية واللاواعية الحاضرة في وسطنا المدرسي، ومن الناحية المنهجية عبر توظيف منهجية تحليل المضمون في إحصاء ورصد وتصنيف وفهم وتأويل الكتابات على الجدران، محاولين بذلك الإجابة عن السؤال التالي: ما تمظهرات العنف والعدوان في الوسط المدرسي من خلال كتابات التلاميذ على الجدران؟ وما المجالات (التيمات) التي تنتمي إليها هذه الكتابات بشكل عام؟ ثم، ما المجالات (التيمات) الموجهة لمشاعر العنف والعدوان لدى التلاميذ؟

W. S. Conradie​​​​​​​, P. Wolski, B. C. Hewitson

<p>The 2014–2018 drought over South Africa's winter rainfall zone (WRZ) created a critical water crisis which highlighted the region's drought and climate change vulnerability. Consequently, it is imperative to better understand the climatic characteristics of the drought in order to inform regional adaptation to projected climate change. In this paper we investigate the spatio-temporal patterns of drought intensity and the recent rainfall trends, focusing on assessing the consistency of the prevailing conceptual model of drought drivers with observed patterns. For this we use the new spatial subdivision for the region encompassing the WRZ introduced in our companion paper <span class="cit" id="xref_paren.1">(<a href="#bib1.bibx13">Conradie et al.</a>, <a href="#bib1.bibx13">2022</a>)</span>.</p> <p>Compared to previous droughts since 1979, the 2014–2018 drought in the WRZ core was characterised by a markedly lower frequency of very wet days (exceeding the climatological 99.5th percentile daily rainfall – including dry days) and of wet months (<span class="inline-formula">SPI₁&gt;0.5</span>), a sub-seasonal attribute not previously reported. There was considerable variability in the spatial footprint of the drought. Short-term drought began in the south-western core WRZ in spring 2014. The peak intensity gradually spread north-eastward, although a spatially near-uniform peak is seen during mid-2017. The overall drought intensity for the 2015–2017 period transitions radially from most severe in the WRZ core to least severe in the surroundings. During 2014 and 2015, the drought was most severe at those stations receiving the largest proportion of their rainfall from westerly and north-westerly winds; by 2018, those stations receiving the most rain from the south and south-east were most severely impacted. This indicates an evolving set of dynamic drivers associated with distinct rain-bearing synoptic flows.</p> <p>No evidence is found to support the suggestion that the drought was more severe in the mountain catchments of Cape Town's major supply reservoirs than elsewhere in the core nor that rain day frequency trends since 1979 are more negative in this subdomain. Rainfall and rain day trend rates also exhibit some connections to the spatial seasonality structure of the WRZ, although this is weaker than for drought intensity. Caution should be applied in assessing South African rain day trends given their high sensitivity to observed data shortcomings. Our findings suggest an important role for zonally asymmetric dynamics in the region's drought evolution. This analysis demonstrates the utility of the spatial subdivisions proposed in the companion paper by highlighting spatial structure in drought intensity evolution linked to rainfall dynamics.</p>

Ismail Hamed Elsanousi

In this paper we studied stochastic delayed differential equations driven by Le’vy noise. The analogue of Ito formula is considered. The Black-Scholes formula analogue for Vanilla call option price formula is derived.

Henrietta Nkansah, Francis Benyah, Henry Amankwah

The paper considers the problem of least squares minimization with L1-norm regularization functional. It investigates various smoothing approximations for the L1-norm functional. It considers Quadratic, Sigmoid and Cubic Hermite functionals. A Tikhonov regularization is then applied to each of the resulting smooth least squares minimization problem. Results of numerical simulations for each smoothing approximation are presented. The results indicate that our regularization method is as good as any other non-smoothing method used in developed solvers.

Su Jiang, Mun-Hong Hui, Louis J. Durlofsky

Data-space inversion (DSI) is a data assimilation procedure that directly generates posterior flow predictions, for time series of interest, without calibrating model parameters. No forward flow simulation is performed in the data assimilation process. DSI instead uses the prior data generated by performing O(1000) simulations on prior geomodel realizations. Data parameterization is useful in the DSI framework as it enables representation of the correlated time-series data quantities in terms of low-dimensional latent-space variables. In this work, a recently developed parameterization based on a recurrent autoencoder (RAE) is applied with DSI for a real naturally fractured reservoir. The parameterization, involving the use of a recurrent neural network and an autoencoder, is able to capture important correlations in the time-series data. RAE training is accomplished using flow simulation results for 1,350 prior model realizations. An ensemble smoother with multiple data assimilation (ESMDA) is applied to provide posterior DSI data samples. The modeling in this work is much more complex than that considered in previous DSI studies as it includes multiple 3D discrete fracture realizations, three-phase flow, tracer injection and production, and complicated field-management logic leading to frequent well shut-in and reopening. Results for the reconstruction of new simulation data (not seen in training), using both the RAE-based parameterization and a simpler approach based on principal component analysis (PCA) with histogram transformation, are presented. The RAE-based procedure is shown to provide better accuracy for these data reconstructions. Detailed posterior DSI results are then presented for a particular “true” model (which is outside the prior ensemble), and summary results are provided for five additional “true” models that are consistent with the prior ensemble. These results again demonstrate the advantages of DSI with RAE-based parameterization for this challenging fractured reservoir case.

Khetam Alzubaidy, Osama Hannon

ان دراسة الجسیمات المعلقة (Particular matter (PM₁₀)) والتکهن بها ضروری للتقلیل والسیطرة على الأضرار البیئیة وصحة الانسان. هنالک العدید من مصادر التلوث او ما یسمى بالملوثات والتی ربما تؤثر على متغیر PM₁₀. کل هذه المتغیرات تصنف بیاناتها کغیر خطیة. اخذ بیانات الدراسة من محطة مناخیة فی مالیزیا. وتم استخدام نماذج الانحدار  الخطی المتعدد Multiple linear regression (MLR) کطریقة إحصائیة خطیة للتنبؤ بمتغیر PM₁₀ من خلال تأثره  بمتغیرات الأرصاد الجویة المقابلة، لذلک فقد یعکس نتائج غیر دقیقة عند استخدامه مع مجموعات البیانات غیر الخطیة. ولتحسین نتائج التنبؤ تم استخدام الشبکات العصبیة المعاودةRecurrent neural network (RNN)  من  خلال توفیقه مع نموذج MLR ضمن الطریقة الهجینة MLR-RNN. وکذلک تم استخدام تحلیل المویجات Wavelet فی ترشیح النتائج المستحصلة من طریقة MLR-RNN للحصول على تحسین اکثر للنتائج التنبؤ من خلال ما یسمى الطریقة الهجینة  RNN-Wavelet واعتماداً على نموذج MLR. ان افضل نتائج التنبؤ بشکل عام کانت باستخدام الطریقة الهجینة  RNN-Wavelet.

CNP Slagle

Herein we present one hundred inequalities culled from various corners of the probability, statistics, and combinatorics literature. We welcome new suggestions.

Yuye Zou, Guoliang Fan, Riquan Zhang

In this thesis, we establish non-linear wavelet density estimators and studying the asymptotic properties of the estimators with data missing at random when covariates are present. The outstanding advantage of non-linear wavelet method is estimating the unsoothed functions, however, the classical kernel estimation cannot do this work. At the same time, we study the larger sample properties of the ISE for hazard rate estimator.

Elham Nazari, Hamed Tabesh

Introduction: The coronavirus outbreak has become a serious issue of the entire world. In some ways, the ability to provide outbreak rate prediction is helpful. Therefore the main purpose of this study was to investigate the incidence pattern of Confirmed COVID-19 Cases in Iran, and comparison between countries with high infected person such as China, Italy and South Korea. Method: In this cross sectional study 126789 infected cases with COVID 19 related countries with highest infection, China, Italy, Iran and South Korea in 30 day timespan was extracted from the cumulative frequency chart at https://www.worldmeters. Info/coronavirus/. The incidence rate pattern was presented. Results: The findings show the frequency pattern of the infected person’s frequency within 30 days since the first case has observed in Iran are similar. Although incidence rate coronavirus is similar to other countries in during 14 days, but after the 14th day, there is a noticeable difference between the obtained pattern of confirmed cases in Iran and other countries. There is a spectacular difference in the number of patients in Iran and South Korea after the seventh day and between Iran and Italy after the fourteenth day. Conclusion: The Covid-19 quickly spread across the world and caused varying challenges. Thus the prevention strategies aimed at reducing transmission in the community are a necessity.

Ros Idayuwati Alaudin, Noriszura Ismail, Zaidi Isa

The objective of this study is to use the Bayesian quantile regression for studying the retirement consumption puzzle, which is defined as the drop in consumption upon retirement, using the cross-sectional data of the Malaysian Household Expenditure Survey (HES) 2009/2010. Three different measures of consumption, namely, total expenditure, work-related expenditure, and nonwork-related expenditure, are suggested for studying the retirement consumption puzzle. The results show that the drop in consumption upon retirement is significant and has a regressive distributional effect as indicated by larger drops at lower percentiles and smaller drops at higher percentiles. The smaller drops among higher consumption retirees (or higher income retirees) may imply that they have more savings and/or retirement benefits than the smaller consumption retirees (or lower income retirees). Comparison between the three types of consumption shows that the work-related expenditure has a uniform drop across the distribution. The drop under the nonwork-related expenditure varies across the distribution, implying that it is the source behind the variation of the consumption drop.

Budyanra Budyanra, Ghaida Nasria Azzahra

Province of Aceh has basic immunization coverage toddler lowest in Indonesia in 2015. even though, this province has Posyandu and Puskesmas ratio per population of the highest in the western region of Indonesia. This data their concerns regarding immunization coverage has not been handled well in Aceh Province. This papers aims to identify variables that affect the status of complete basic immunization of children aged 12-59 months in Aceh by using ordinal logistic regression analysis. Ordinal logistic regression model used is proportional odds models. Data are obtained from Susenas 2015 that was held in March 2015 by BPS-Statistic of Indonesia. Based on the results of processing data, known only 37.7% of children aged 12-59 months in the province of Aceh in 2015 which gets fully immunized, the remaining 50.6% receive primary immunization but is not complete, even about 11.7% have not received basic immunization at all. From the proportional odds model results showed that the number of children born to mothers (odds ratio = 0.88), maternal age at delivery (odds ratio = 1.03), the level of maternal education (odds ratio = 1.22), and the educational level of the household (odds ratio = 1,2) have a significant impact on the status of complete basic immunization of children. Future studies are expected to include the element of timeliness and add other variables and also with other models in ordinal logistic regression. Keywords: Immunization, Ordinal Logistic Regression, Proportional Odds, Susenas

P. Laplace

G. Taraldsen, B. Lindqvist

ABSTRACT According to Jeffreys improper priors are needed to get the Bayesian machine up and running. This may be disputed, but usage of improper priors flourish. Arguments based on symmetry or information theoretic reference analysis can be most convincing in concrete cases. The foundations of statistics as usually formulated rely on the axioms of a probability space, or alternative information theoretic axioms that imply the axioms of a probability space. These axioms do not include improper laws, but this is typically ignored in papers that consider improper priors. The purpose of this paper is to present a mathematical theory that can be used as a foundation for statistics that include improper priors. This theory includes improper laws in the initial axioms and has in particular Bayes theorem as a consequence. Another consequence is that some of the usual calculation rules are modified. This is important in relation to common statistical practice which usually include improper priors, but tends to use unaltered calculation rules. In some cases, the results are valid, but in other cases inconsistencies may appear. The famous marginalization paradoxes exemplify this latter case. An alternative mathematical theory for the foundations of statistics can be formulated in terms of conditional probability spaces. In this case, the appearance of improper laws is a consequence of the theory. It is proved here that the resulting mathematical structures for the two theories are equivalent. The conclusion is that the choice of the first or the second formulation for the initial axioms can be considered a matter of personal preference. Readers that initially have concerns regarding improper priors can possibly be more open toward a formulation of the initial axioms in terms of conditional probabilities. The interpretation of an improper law is given by the corresponding conditional probabilities.

Vahid Nekoukhou, Hamid Bidram

In this paper, the researchers attempt to introduce a new generalization of the exponential distribution. This new model is obtained by compounding the exponential distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution. The new introduced model contains the exponential-geometric distribution as a special case. Some basic distributional properties, moments and order statistics of the new model are discussed. Estimation of the parameters is illustrated, using the maximum likelihood method, and the model with a real data set is also examined.