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Dimensionality Reduction (DR) is the process of reducing the numerous features or random variables under consideration to a limited number of features by obtaining a set of principal variables. These techniques cater great values in machine learning, which come in handy to simplify a classification or a regression dataset, thereby yielding a better-performing predictive model. Techniques used for DR include Feature Selection methods, Matrix Factorization, AutoEncoder methods, and Manifold Learning. Merits of DR include data compression, reduced space of storage, and removal of redundant features. This paper attempts to review various techniques used to carry out dimensionality reduction while providing an exhaustive comparative study over the merits and demerits of each of the techniques used under the empirical experiments performed by the authors whose work is being reviewed. [ABSTRACT FROM AUTHOR]

Obeid and Kadry (2019) tried to study the product and quotient of the independent Pareto and Rayleigh random variables. The distributions they obtained are incorrect and in fact there is no closed form distributions as discussed here. We will mention the errors made and try to establish the correct versions of the probability density functions of these distributions for the truncated Pareto and Rayleigh random variables. [ABSTRACT FROM AUTHOR]

• The citations of 729,515 articles fit by the generalized extreme-value distribution. • The complexity of references and citations of papers' quantiles is studied. • The macroscopic model of the citation distribution is proposed. The paper presents an in-depth study of uncited papers. For that, we explore the documents indexed in the INSPIRE database from 1970 to 2015. Uncited articles represent a complex bibliometric environment in which references are generated. The reference lists of uncited papers form a dynamic system partially responsible for the redistribution of scientific impact. Our task is to quantify the detailed structure of citations and references directly in terms of quantiles. We also study the entropy and the statistical complexity measure of references and citations of papers' quantiles. We introduce a theoretical framework in which citation distribution is considered an asymptotic distribution of the largest values in a sequence of independent identically distributed random variables. We show that this asymptotic distribution is the generalized extreme-value distribution. Furthermore, we empirically demonstrate that the asymptotic behavior of citation distribution is close to (but not quite) the generalized extreme-value distribution. [ABSTRACT FROM AUTHOR]

The study of the dynamics of the size of a population via mathematical modelling is a problem of interest and widely studied. Traditionally, continuous deterministic methods based on differential equations have been used to deal with this problem. However, discrete versions of some models are also available and sometimes more adequate. In this paper, we randomize the Pielou logistic equation in order to include the inherent uncertainty in modelling. Taking advantage of the method of transformation of random variables, we provide a full probabilistic description to the randomized Pielou logistic model via the computation of the probability density functions of the solution stochastic process, the steady state, and the time until a certain level of population is reached. The theoretical results are illustrated by means of two examples: The first one consists of a numerical experiment and the second one shows an application to study the diffusion of a technology using real data. [ABSTRACT FROM AUTHOR]

A new robust Kalman filter (KF) based on mixing distribution is presented to address the filtering issue for a linear system with measurement loss (ML) and heavy-tailed measurement noise (HTMN) in this paper. A new Student's t -inverse-Wishart-Gamma mixing distribution is derived to more rationally model the HTMN. By employing a discrete Bernoulli random variable (DBRV), the form of measurement likelihood function of double mixing distributions is converted from a weighted sum to an exponential product, and a hierarchical Gaussian state-space model (HGSSM) is therefore established. Finally, the system state, the intermediate random variables (IRVs) of the new STIWG distribution, and the DBRV are simultaneously estimated by utilizing the variational Bayesian (VB) method. Numerical example simulation experiment indicates that the proposed filter in this paper has superior performance than current algorithms in processing ML and HTMN. [ABSTRACT FROM AUTHOR]

We consider a principal who periodically offers a fixed and costly nonmonetary reward to agents to incentivize them to invest effort over the long run. An agent's output, as a function of his effort, is a priori uncertain and is worth a fixed per-unit value to the principal. The principal's goal is to design an attractive reward policy that specifies how the rewards are to be given to an agent over time based on that agent's past performance. This problem, which we denote by P , is motivated by practical examples from both academia (e.g., a reduced teaching load) and industry (e.g., "Supplier of the Year" awards). The following "limited-term" (LT) reward policy structure has been quite popular in practice. The principal evaluates each agent periodically; if an agent's performance over a certain (limited) number of periods in the immediate past exceeds a predefined threshold, then the principal rewards him for a certain (limited) number of periods in the immediate future. When agents' outputs are deterministic in their efforts, we show that there always exists an optimal policy that is an LT policy and also, obtain such a policy. When agents' outputs are stochastic, we show that the class of LT policies may not contain any optimal policy of problem P but is guaranteed to contain policies that are arbitrarily near optimal. Given any ϵ > 0 , we show how to obtain an LT policy whose performance is within ϵ of that of an optimal policy. This guarantee depends crucially on the use of sufficiently long histories of the agents' outputs. We also analyze LT policies with short histories and derive structural insights on the role played by (i) the length of the available history and (ii) the variability in the random variable governing an agent's output. We show that the average performance of these policies is within 5% of the optimum, justifying their popularity in practice. We then introduce and analyze the class of "score-based" reward policies; we show that this class is guaranteed to contain an optimal policy and also, obtain such a policy. Finally, we analyze a generalization in which the principal has a limited number for rewards in any given period and show that the class of score-based policies, with modifications to accommodate the limited availability of the rewards, continues to contain an optimal solution for the principal. This paper was accepted by Jeannette Song, operations management. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4482. [ABSTRACT FROM AUTHOR]

Most peer-evaluation practices rely on the evaluator’s goodwill and model them as potentially noisy evaluators. But what if graders are competitive, i.e., enjoy higher utility when their peers get lower scores? We model the setting as a multi-agent incentive design problem and propose a new mechanism, PEQA, that incentivizes these agents (peer-graders) through a score-assignment rule and a grading performance score. PEQA is designed in such a way that it makes grader-bias irrelevant and ensures grader-utility to be monotonically increasing with the grading-precision, despite competitiveness. When grading is costly and costs are private information of the individual graders, a modified version of PEQA implements the socially optimal grading-choices in equilibrium. Data from our classroom experiments is consistent with our theoretical assumptions and show that PEQA outperforms the popular median mechanism, which is used in several massive open online courses (MOOCs). [ABSTRACT FROM AUTHOR]

We introduce a fundamental lemma called the Poisson matching lemma, and apply it to prove one-shot achievability results for various settings, namely channels with state information at the encoder, lossy source coding with side information at the decoder, joint source-channel coding, broadcast channels, distributed lossy source coding, multiple access channels and channel resolvability. Our one-shot bounds improve upon the best known one-shot bounds in most of the aforementioned settings (except multiple access channels and channel resolvability, where we recover bounds comparable to the best known bounds), with shorter proofs in some settings even when compared to the conventional asymptotic approach using typicality. The Poisson matching lemma replaces both the packing and covering lemmas, greatly simplifying the error analysis. This paper extends the work of Li and El Gamal on Poisson functional representation, which mainly considered variable-length source coding settings, whereas this paper studies fixed-length settings, and is not limited to source coding, showing that the Poisson functional representation is a viable alternative to typicality for most problems in network information theory. [ABSTRACT FROM AUTHOR]

Nofal and El Gebaly (2017), presented certain characterizations of the Pareto distribution based on the conditional expectations of power of the order statistics. In this very short note we show that the same results can easily be obtained in terms of the power of the random variable. [ABSTRACT FROM AUTHOR]

It is pointed out that a general theorem presented in Yu Miao and Shoufang Xu's paper has a serious gap. In this small note, a counterexample for this theorem is provided exhibiting a triangular array of real numbers and a sequence of independent identically distributed random variables for which its conclusion fails. An reformulation of Yu Miao and Shoufang Xu's general theorem is performed making this statement true. [ABSTRACT FROM AUTHOR]

Security of linear ramp secret sharing schemes can be characterized by the relative generalized Hamming weights of the involved codes. In this paper, we elaborate on the implication of these parameters and devise a method to estimate their value for general one-point algebraic geometric codes. As it is demonstrated, for Hermitian codes, our bound is often tight. Furthermore, for these codes, the relative generalized Hamming weights are often much larger than the corresponding generalized Hamming weights. [ABSTRACT FROM AUTHOR]

This paper is focused on observational data and on the use of large data sets to implement an experimental design without additional runs, for an efficient use of these data. More specifically, the proposed procedure is based on several steps, aimed at avoiding some problems, such as lack of randomization and efficiency, obtaining a final experimental design that can be assumed as optimal from the point of view of a sequential optimality. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Note, for instance, that the probabilities given by Castellares et al. ([1]) in page 4 are the same than those shown in expression (9.115) in the book by Johnson et al. ([3]), with the change of parameters Graph HT ht and Graph HT ht Neyman type A (NTA) distribution is frequently used in Biology, Biodosimetry, Environmental Sciences, Epidemiology, etc. A count random variable I X i is said to follow a stopped-sum Poisson, compound Poisson, multiple Poisson or clustered-Poisson distribution, if it can be represented as Graph HT ht where I N i is a Poisson random variable with parameter Graph HT ht and Graph HT ht are independent, identically distributed random variables that are also independent of I N i . [Extracted from the article]

The 2022 International Symposium on Nonparametric Statistics was held in Paphos, Cyprus and co-sponsored by the Institute of Mathematical Statistics and the Bernoulli Society of Mathematical Statistics and Probability. The symposium brought together researchers from around the world to discuss recent advances and trends in nonparametric statistics. The conference covered a wide range of topics, including nonparametric estimation, hypothesis testing, adaptive inference, high-dimensional statistical inference, and more. The special issue of the Journal of Nonparametric Statistics contains papers that have undergone a peer review process and cover diverse areas of nonparametric statistics. [Extracted from the article]

This paper discussed the fuzzy reliability of pulping system in paper industry. Pulping system consists of four subsystems such as Digester, Knotter, Deckers, and Openers. These subsystems are working in series. In subsystems Knotter and Openers, one unit is operative and another unit is kept as cold standby. Fuzzy failure rates and fuzzy repair rates of the subsystems are taken as general. Trapezoidal fuzzy numbers are used to find out the reliability of the pulping system. Using Mehar’s method, the numerical results for reliability are obtained by considering exponential, Rayleigh, and Weibull distributions. On the basis of the results obtained in this study, it is suggested that paper industry management should involve Weibull distributed random variables for pulping system to attain higher reliability. [ABSTRACT FROM AUTHOR]

The evidence of soil nonuniformity has been reported in several site investigation reports and is well-confirmed for any soil in general. However, studies related to the spatial soil variability of offshore ground are somewhat limited, and current design practices for monopile foundations also overlook the uncertainty of the offshore ground. This paper presents the probabilistic evaluation of the serviceability limit state of monopile foundations considering the spatial variability of offshore ground. The nonuniformity of the ground is modeled utilizing the site-specific undrained shear strength (su) as a stochastic variable, using a spatially correlated Gaussian random field. A hardening soil constitutive model is utilized in 3D finite element analysis of offshore ground, with a focus on parameter calibration. The reliability of the serviceability limit state is assessed based on the allowable load on the pile head. The stochastic behavior of the maximum bending moment and maximum shear force along the depth of the monopile is also investigated. Besides, the paper also highlights the importance of incorporating ground nonuniformity during the design process of a monopile foundation. [ABSTRACT FROM AUTHOR]

Focuses on the concept of random variable and the nature of a statistical model which is central to the posterior approach of factor analysis. Existence of many linear factor models leading to any given covariance matrix; Fundamental indeterminacy common to all latent variable models; Distinction between a latent profile model and a linear factor model.

This paper develops a methodology for finding minimum energy per bit in networks with correlated information, without at need for finding bounds on capacity. This is used to derive the exact minimum energy per bit for some broadcast and interference channels with common and correlated messages, and bounds on the minimum energy per bit for some other channels. [ABSTRACT FROM PUBLISHER]

This paper studies the multiple-access channel (MAC) with rate-limited feedback. The channel output is encoded into one stream of bits, which is provided causally to the two users at the channel input. An achievable rate region for this setup is derived, based on superposition of information, block Markov coding, and coding with various degrees of side information for the feedback link. The suggested region coincides with the Cover–Leung inner bound for large feedback rates. The result is then extended for cases where there is only a feedback link to one of the transmitters, and for a more general case where there are two separate feedback links to both transmitters. We compute achievable regions for the Gaussian MAC and for the binary erasure MAC. The Gaussian region is computed for the case of common rate-limited feedback, whereas the region for the binary erasure MAC is computed for one-sided feedback. It is known that for the latter, the Cover–Leung region is tight, and we obtain results that coincide with the feedback capacity region for high feedback rates. [ABSTRACT FROM PUBLISHER]

In a recent paper the authors proved a nonuniform local limit theorem concerning normal approximation of the point probabilities P (S = k) when S = ∑ i = 1 n X i and X 1 , X 2 , ... , X n are independent Bernoulli random variables that may have different success probabilities. However, their main result contained an undetermined constant, somewhat limiting its applicability. In this paper we give a nonuniform bound in the same setting but with explicit constants. Our proof uses Stein's method and, in particular, the K-function and concentration inequality approaches. We also prove a new uniform local limit theorem for Poisson binomial random variables that is used to help simplify the proof in the nonuniform case. [ABSTRACT FROM AUTHOR]

This paper provides sets of sufficient conditions for mean convergence theorems for arrays of dependent random variables. We expand and improve a number of particular cases in the literature including Theorem 2.1 in Sung (Appl Math Lett 26(1):18–24, 2013), Theorems 3.1–3.3 in Wu and Guan (J Math Anal Appl 377(2):613–623, 2011), and Theorem 3 in Lita da Silva (Results Math 74(1):1–11, 2019), among others. The proof is different from those in the aforementioned papers and the main results can be applied to obtain mean convergence results for arrays of functions of non-homogeneous Markov chains and dependent bootstrap. [ABSTRACT FROM AUTHOR]

The complementary risk is common and important in the engineering field. However, there is not much research about it because of its complex derivation compared with the competing risk model. In this paper, we concentrate on inference of step-stress partially accelerated life test in the presence of complementary risks under progressive type-II censoring scheme. The Weibull distribution is chosen as the baseline lifetime of the model. The tampered random variable model is adopted as the statistical acceleration model in the accelerated test. We apply both the classical and Bayesian methods to obtain the estimation of lifetime parameters and acceleration factors. The reliability and reversed hazard rate are estimated based on the parametric estimates. The computational formulae of expected total test time are creatively derived under the step-stress and censored setting. The theoretical calculations are compared with simulated values to verify the derivation. Also, numerical studies including the simulation study and real-data analysis in engineering background are conducted to compare and illustrate the performance of the approaches proposed in the paper. Some conclusions and suggestions for actual production are given at the end of the paper. [ABSTRACT FROM AUTHOR]

The framework of this paper was intertemporal choice, that is to say, the process whereby people were required to choose between a smaller-sooner reward and a larger-later income. In this study, the selection of rewards was supported by a discount function instead of direct preferences between the involved rewards. The objective of this paper was to measure the discounting concentration of a discount function through a variant of the Gini index and the Lorenz curve usually used in statistics. Both measures allowed for the comparison of the discounting concentration corresponding to two discount functions. The methodology employed in this paper was based on the parallelism between a discount function and the distribution function of an absolutely continuous random variable. This similarity allowed us to export the measures of concentration from the field of statistics to finance. The main result of this work was the analysis of the discounting concentration depending on other characteristics of the shape of a discount function (regularity and super-additivity) and the total area under the discount function curve. [ABSTRACT FROM AUTHOR]

The article focuses on the system reliability analysis of steel trusses (plane and spatial). The computations are realized by the use of a developed by the author C++ code. The following loads are taken into account: self-weight, weight of coverings, wind and snow. The limit state function is defined as a difference between the bearing capacity and the effect of action of an element. The paper presents how effective tool is the system reliability analysis compared with traditional structural design methods. The methods of transforming Gumbel distribution into normal and generating random variables are described. [ABSTRACT FROM AUTHOR]

Nowadays, one of the main challenges facing green innovation management is how to enhance the performance of innovation processes by utilizing asymmetric input and output data. Therefore, this paper develops an improved SBM model analysis framework for evaluating the green innovation efficiency of asymmetric input and output data. The framework is applied to assess the technical (TE), managerial (PTE), and scale (SE) efficiencies of new energy companies under three input variables (R&D personnel input, R&D capital input, and comprehensive energy consumption input), two desirable output variables (green technology output and economic output), and one undesirable output variable (greenhouse gas emissions). Then, environmental factors and random factors are eliminated from the obtained input slack variables based on the SFA model, placing decision-making units in a homogeneous environment. The results demonstrate that TE, PTE, and SE are improved after eliminating environmental factors and random factors. Subsequently, based on the entropy method, this paper classifies companies' green innovation patterns into four categories and provides targeted solutions. The purpose of this paper is to provide an evaluation method for new energy companies to understand green innovation efficiency and assist decision makers in identifying the most optimal resource allocation approach. The proposed improved SBM model contributes to the literature and to industry practice by (1) providing a reliable evaluation of green innovation efficiency under asymmetric input and output data; (2) determining effective improvement actions based on a slack analysis of environmental variables and random variables that lead to improved process performance; and (3) making fuzzy innovation performance efficient to facilitate understanding and managing innovation resource allocation quality. [ABSTRACT FROM AUTHOR]

We would like to point out that the formula for the cumulative distribution given in Coelho-Barros et al. (2017) and a similar version of it given in Usman et al. (2021) are not cumulative distribution functions as these functions do not satisfy the one or more necessary and sufficient conditions for a function to be a cumulative distribution function. We would also like to mention that formulas for the cumulative distribution functions of product and ratio of two independent Pareto and Exponential random variables given by Obeid and Kadry (2022) are not cumulative distribution functions either. We do not believe that these formulas can be fixed to be cumulative distribution functions. In this short article, we provide mathematical justification in support of these claims. [ABSTRACT FROM AUTHOR]

This scientific paper explores the operation of a multiprocessor task servicing system. Tasks are received into the system at random intervals and are characterized by several stochastic parameters, including the number of processors required for their execution, the maximum allowable busy time for these processors, and the permissible waiting time in the task queue. The organization of task servicing in this system follows a first-in, first-out (FIFO) approach, ensuring uninterrupted processing. The key servicing process involves periodically selecting the first task in the queue and assessing its feasibility for immediate execution. If the task meets the necessary criteria, it is dispatched for processing. This process continues iteratively until a task is found, the parameters of which prevent immediate servicing. It is important to note that tasks in the queue have a limited window of time within which they can be serviced; otherwise, they may exit the system without service. This paper focuses on systems characterized by exponential distributions for random variables related to task arrivals, servicing times, and waiting restrictions. A system of equations is derived that describes the system's steady-state behavior. These equations enable the calculation of probabilities associated with the system's various states. Additionally, the paper provides insights into the probability distributions of virtual waiting times for tasks that arrive in the system at any given moment. [ABSTRACT FROM AUTHOR]