Hasil untuk "Probabilities. Mathematical statistics"

Emilio Gómez-Déniz, Enrique Calderín-Ojeda, José M. Sarabia

A transformation of a density function is introduced to derive two families of continuous densities, the first symmetric and the second not-necessarily symmetric, exhibiting both unimodality and bimodality. Their respective density functions are provided in closed form, allowing us to simply obtain moments and related quantities. We focus on the case where the normal distribution is considered, although it can be applied to other models, such as the logistic and Cauchy distributions. This transformation is also extended to derive a family of asymmetric unimodal and bimodal distributions via Azzalini’s scheme. An example related to environmental science illustrate these models’ practical performance.

Durvudkhan Suragan, Bolys Sabitbek

Nazarbayev University in Astana, Kazakhstan, will host the 15th International ISAAC Congress from July 21–25, 2025. The International Society for Analysis, its Applications, and Computation (ISAAC) Congress is a prestigious event that continues a successful series of meetings previously held across the globe.

Adimias Wendimagegn Agegnehu, Ayele Taye Goshu, Butte Gotu Arero

The main purpose of this paper is to introduce a new alpha power transformed beta probability distribution that reveals interesting properties. The studuy provide a comprehensive explanation of the statistical characteristics of this innovative model. Various properties of the new distribution were derived, using the baseline beta distribution, statistical techniques, and probabilistic axioms. These include the probability density, cumulative distribution, survival function, hazard function, moments about the origin, moment generating function, and order statistics. For parameter estimation, the maximum likelihood estimation method using Newton Raphson numerical technique is employed. To evaluate the performance of our estimation method, the mean squared errors of the estimated parameters for different simulated sample sizes are used. In addition simulation studies of the new distribution are conducted to demonstrate the behavior of the probability model. To demonstrate the practical utility and flexibility of the alpha power transformed beta distribution, it is fitted to two real-life datasets and compared to commonly known probability distributions such as the Weibull, exponential Weibull, Beta, and Kumaraswamy beta distributions. It offers a superior fit to the data considered. The distribution reviales of the microbes reveald a wide range of shapes of probability density functions and flexible hazard rates. The distribution is a new contribution to the field of statistical and probability theory. The findings of the study can be used as a basis for future research in the area of statistical science and health.

Scott E. Field, Scott E. Field, Sigal Gottlieb et al.

Amit N. Kumar

In this paper, we develop Stein's method for negative binomial distribution using call function defined by fz(k) = (k - z)+ = max{k - z, 0}, for k ≥ 0 and z ≥ 0. We obtain error bounds between E [ fz(Nr,p)] and E [ fz(V )], where Nr,p follows negative binomial distribution and V is the sum of locally dependent random variables, using certain conditions on moments. We demonstrate our results through an interesting application, namely, collateralized debt obligation (CDO), and compare the bounds with the existing bounds.

Chris R. Surfus

AbstractFor the first time ever, the United States Census Bureau began collecting data on the LGBT community with Phase 3.2 of the Household Pulse Survey. The Household Pulse Survey assesses how residents of the United States are doing during the COVID-19 pandemic. The data provided by the Household Pulse Survey Week 34 through Week 39 provides information to understand the lives of LGBT residents of the United States and how the LGBT community as a whole is doing economically. This study merges six weeks of the Household Pulse Survey, for a total of 382,908 survey responses. The sample represents a population of 250,265,449 adult residents aged 18 and older in the United States. This study provides the first nationally representative sample of residents of the United States that identify as transgender. This study specifically focuses on LGBT people with disabilities but highlights disparities facing transgender disabled U.S. adult residents. Disability is defined in the Household Pulse Survey as a severe or total impairment of those with seeing, hearing, remembering, and mobility disability types. The data indicates significant disparities for LGBT people compared to non-LGBT people, specifically in terms of economic considerations like work loss, household finances, and mental health.

M. Taniguchi, Yoshihide Kakizawa

Andrew Gelman, Shira Mitchell, Jeffrey Sachs et al.

The Millennium Villages Project was an integrated rural development program carried out for a decade in 10 clusters of villages in sub-Saharan Africa starting in 2005, and in a few other sites for shorter durations. An evaluation of the 10 main sites compared to retrospectively chosen control sites estimated positive effects on a range of economic, social, and health outcomes (Mitchell et al. ). More recently, an outside group performed a prospective controlled (but also nonrandomized) evaluation of one of the shorter-duration sites and reported smaller or null results (Masset et al. ). Although these two conclusions seem contradictory, the differences can be explained by the fact that Mitchell et al. studied 10 sites where the project was implemented for 10 years, and Masset et al. studied one site with a program lasting less than 5 years, as well as differences in inference and framing. Insights from both evaluations should be valuable in considering future development efforts of this sort. Both studies are consistent with a larger picture of positive average impacts (compared to untreated villages) across a broad range of outcomes, but with effects varying across sites or requiring an adequate duration for impacts to be manifested.

Aiyared Iampan, V. Vijaya Bharathi, M. Vanishree et al.

In this paper, the concept of interval-valued intuitionistic fuzzy sets to subalgebras and ideals of Hilbert algebras is introduced. The inverse image of interval-valued intuitionistic fuzzy subalgebras and interval-valued intuitionistic fuzzy ideals of Hilbert algebras is studied and some related properties are investigated. Equivalence relations on interval-valued intuitionistic fuzzy ideals are discussed.

Mohd Nizam Osman, Muhammad Haika Faeq Ismail, Khairul Anwar Sedek et al.

Home security is a critical issue, especially for the civilians to protect their property from harm. Currently, the increase in home breaking usually occurs during school holidays and public holiday seasons. Therefore, to overcome the problem and the main objective is to design and develop a low-cost home security notification system using PIR sensor to detect movement of intruders, Raspberry Pi Camera, GPS module integrated with Raspberry Pi Zero WH to send an alert notification message with image, date, location, and time via Telegram Bot to the house owner’s and people nearby through a smart phone. The system utilizes the System Development Life Cycle (SDLC) by implementing the waterfall model as the methodology. Three experiments were conducted to examine the effectiveness of the system which is sensor detection range, response time and user acceptance test (UAT). The finding indicates that the home security notification system was efficient, effective, low-cost, and easy to use. Besides, the system can detect the presence of the intruder and send the notification message in a reasonable time. Meanwhile, the result from the UAT indicates that the proposed system has a positive impact and to be well accepted by the majority of the users. Hence, the system can help the house owners to take immediate action such as calling the neighbourhood association or police department authority when the system detects an intruder in the house. 

P. Marinho, Rodrigo B. Silva, M. Bourguignon et al.

Several lifetime distributions have played an important role to fit survival data. However, for some of these models, the computation of maximum likelihood estimators is quite difficult due to presence of flat regions in the search space, among other factors. Several well-known derivative-based optimization tools are unsuitable for obtaining such estimates. To circumvent this problem, we introduce the AdequacyModel computational library version 2.0.0 for the R statistical environment with two major contributions: a general optimization technique based on the Particle Swarm Optimization (PSO) method (with a minor modification of the original algorithm) and a set of statistical measures for assessment of the adequacy of the fitted model. This library is very useful for researchers in probability and statistics and has been cited in various papers in these areas. It serves as the basis for the Newdistns library (version 2.1) published in an impact journal in the area of computational statistics, see https://CRAN.R-project.org/package=Newdistns. It is also the basis of the Wrapped library (version 2.0), see https://CRAN.R-project.org/package=Wrapped. A third package making use of the AdequacyModel library can be found in https://CRAN.R-project.org/package=sglg. In addition, the proposed library has proved to be very useful for maximizing log-likelihood functions with complex search regions. The library provides a greater control of the optimization process by introducing a stop criterion based on a minimum number of iterations and the variance of a given proportion of optimal values. We emphasize that the new library can be used not only in statistics but in physics and mathematics as proved in several examples throughout the paper.

A. Zhang, Harrison H. Zhou

Recently network analysis has gained more and more attentions in statistics, as well as in computer science, probability, and applied mathematics. Community detection for the stochastic block model (SBM) is probably the most studied topic in network analysis. Many methodologies have been proposed. Some beautiful and significant phase transition results are obtained in various settings. In this paper, we provide a general minimax theory for community detection. It gives minimax rates of the mis-match ratio for a wide rage of settings including homogeneous and inhomogeneous SBMs, dense and sparse networks, finite and growing number of communities. The minimax rates are exponential, different from polynomial rates we often see in statistical literature. An immediate consequence of the result is to establish threshold phenomenon for strong consistency (exact recovery) as well as weak consistency (partial recovery). We obtain the upper bound by a range of penalized likelihood-type approaches. The lower bound is achieved by a novel reduction from a global mis-match ratio to a local clustering problem for one node through an exchangeability property.

Rosemary Callingham, J. Watson

Strobl Eric V., Zhang Kun, Visweswaran Shyam

Constraint-based causal discovery (CCD) algorithms require fast and accurate conditional independence (CI) testing. The Kernel Conditional Independence Test (KCIT) is currently one of the most popular CI tests in the non-parametric setting, but many investigators cannot use KCIT with large datasets because the test scales at least quadratically with sample size. We therefore devise two relaxations called the Randomized Conditional Independence Test (RCIT) and the Randomized conditional Correlation Test (RCoT) which both approximate KCIT by utilizing random Fourier features. In practice, both of the proposed tests scale linearly with sample size and return accurate p-values much faster than KCIT in the large sample size context. CCD algorithms run with RCIT or RCoT also return graphs at least as accurate as the same algorithms run with KCIT but with large reductions in run time.

Mark A. Wolters

Autologistic regression is an important probability model for dichotomous random variables observed along with covariate information. It has been used in various fields for analyzing binary data possessing spatial or network structure. The model can be viewed as an extension of the autologistic model (also known as the Ising model, quadratic exponential binary distribution, or Boltzmann machine) to include covariates. It can also be viewed as an extension of logistic regression to handle responses that are not independent. Not all authors use exactly the same form of the autologistic regression model. Variations of the model differ in two respects. First, the variable coding—the two numbers used to represent the two possible states of the variables—might differ. Common coding choices are (zero, one) and (minus one, plus one). Second, the model might appear in either of two algebraic forms: a standard form, or a recently proposed centered form. Little attention has been paid to the effect of these differences, and the literature shows ambiguity about their importance. It is shown here that changes to either coding or centering in fact produce distinct, non-nested probability models. Theoretical results, numerical studies, and analysis of an ecological data set all show that the differences among the models can be large and practically significant. Understanding the nature of the differences and making appropriate modeling choices can lead to significantly improved autologistic regression analyses. The results strongly suggest that the standard model with plus/minus coding, which we call the symmetric autologistic model, is the most natural choice among the autologistic variants.

A. Zemanian

M. Kotani, Susumu Ikeda

Abstract Our world is transforming into an interacting system of the physical world and the digital world. What will be the materials science in the new era? With the rising expectations of the rapid development of computers, information science and mathematical science including statistics and probability theory, ‘data-driven materials design’ has become a common term. There is knowledge and experience gained in the physical world in the form of know-how and recipes for the creation of material. An important key is how we establish vocabulary and grammar to translate them into the language of the digital world. In this article, we outline how materials science develops when it encounters mathematics, showing some emerging directions.

M. Masoom Ali, Manisha Pal, Jungsoo Woo

In this paper we consider estimation of R = P(Y < X), when X and Y are distributed as two independent four-parameter generalized gamma random variables with same location and scale parameters. A modified maximum likelihood method and a Bayesian technique have been used to estimate R on the basis of independent samples. As the Bayes estimator cannot be obtained in a closed form, it has been implemented using importance sampling procedure. A simulation study has also been carried out to compare the two methods.

Jose María Fernández-Ponce, Alfonso Suárez-Lloréns

For a one-dimensional probability distribution, the classical concept of central region as a real interquantile interval arises in all applied sciences. We can find applications, for instance, with dispersion, skewness and detection of outliers. All authors agree with the main problem in a multivariate generalization: there does not exist a natural ordering in n-dimensions, n > 1. Because of this reason, the great majority of these generalizations depend on their use. We can say that is common to generalize the concept of central region under the definition of the well known concept of spatial median. In our work, we develop an intuitive concept which can be interpreted as level curves for distribution functions and this one provides a trimmed region. Properties referred to dispersion and probability are also studied and some considerations on more than two dimensions are also considered. Furthermore, several estimations for bivariate data based on conditional quantiles are discussed.

M. M. Mohie EL-Din, M. M. Amein, Nahed S. A. Ali et al.

For a system, which is observed at time t, the residual and past entropies measure the uncertainty about the remaining and the past life of the distribution, respectively. In this paper, we have presented the residual and past entropy of Morgenstern family based on the concomitants of the different types of generalized order statistics (gos) and give the linear transformation of such model. Characterization results for these dynamic entropies for concomitants of ordered random variables have been considered.