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Proportional data arise frequently in a wide variety of fields of study. Such data often exhibit extra variation such as over/under dispersion, sparseness and zero inflation. For example, the hepatitis data present both sparseness and zero inflation with 19 contributing non-zero denominators of 5 or less and with 36 having zero seropositive out of 83 annual age groups. The whitefly data consists of 640 observations with 339 zeros (53%), which demonstrates extra zero inflation. The catheter management data involve excessive zeros with over 60% zeros averagely for outcomes of 193 urinary tract infections, 194 outcomes of catheter blockages and 193 outcomes of catheter displacements. However, the existing models cannot always address such features appropriately. In this paper, a new two-parameter probability distribution called Lindley–binomial (LB) distribution is proposed to analyze the proportional data with such features. The probabilistic properties of the distribution such as moment, moment generating function are derived. The Fisher scoring algorithm and EM algorithm are presented for the computation of estimates of parameters in the proposed LB regression model. The issues on goodness of fit for the LB model are discussed. A limited simulation study is also performed to evaluate the performance of derived EM algorithms for the estimation of parameters in the model with/without covariates. The proposed model is illustrated through three aforementioned proportional datasets. [ABSTRACT FROM AUTHOR]

In unsupervised learning, clustering is a common starting point for data processing. The convex or concave fusion clustering method is a novel approach that is more stable and accurate than traditional methods such as k-means and hierarchical clustering. However, the optimization algorithm used with this method can be slowed down significantly by the complexity of the fusion penalty, which increases the computational burden. This paper introduces a random projection ADMM algorithm based on the Bernoulli distribution and develops a double random projection ADMM method for high-dimensional fusion clustering. These new approaches significantly outperform the classical ADMM algorithm due to their ability to significantly increase computational speed by reducing complexity and improving clustering accuracy by using multiple random projections under a new evaluation criterion. We also demonstrate the convergence of our new algorithm and test its performance on both simulated and real data examples. [ABSTRACT FROM AUTHOR]

Compositional data (CoDa) often appear in various fields such as biology, medicine, geology, chemistry, economics, ecology and sociology. Although existing Dirichlet and related models are frequently employed in CoDa analysis, sometimes they may provide unsatisfactory performances in modelling CoDa as shown in our first real data example. First, this paper develops a multivariate compositional inverse Gaussian (CIG) model as a new tool for analysing CoDa. By incorporating the stochastic representation (SR), the expectation–maximization (EM) algorithm (aided by a one-step gradient descent algorithm) can be established to solve the parameter estimation for the proposed distribution (model). Next, zero observations may be often encountered in the real CoDa analysis. Therefore, the second aim of this paper is to propose a new model (called as ZCIG model) through a novel mixture SR based on both the CIG random vector and a so-called zero-truncated product Bernoulli random vector to model CoDa with zeros. Corresponding statistical inference methods are also developed for both cases without/with covariates. Two real data sets are analysed to illustrate the proposed statistical methods by comparing the proposed CIG and ZCIG models with existing Dirichlet and logistic-normal models. [ABSTRACT FROM AUTHOR]

Technological advancement has led to a dynamic change in how people interact. The interaction can be classified as—social networks (virtual) and real-life (physical) interaction. The relationships among nodes of social networks depend on communication among nodes and have been established by transmitting messages publicly or privately, depending on the trust among nodes. However, it poses three main challenges: (i) nodes can reveal their private message, (ii) private conversation among nodes can be hacked, and (iii) stored messages can be sent to another node, therefore, compromising privacy. The paper presents a privacy-preserving model using two major techniques, Binomial Distribution and Fuzzy Logic. This process has been followed by building predictive models using machine learning to provide potential directions to mitigate security threats posed to social networking platforms. The paper also provides a wholesome discussion of model design for predictive modelling, whereas most state-of-the-art techniques were primarily concerned about delivering potential directions for predictive modelling. The employed statistical and predictive modelling techniques suggest that friendship relationships in real life among people would transcend to ensure a secure and privacy-preserving relationship among them on social networks. Empirical results indicated that XG Boost supersedes the state-of-the-art models by achieving a predictive accuracy of 92.035%. In contrast, introducing new statistical features improves the performance of all our predictive models. [ABSTRACT FROM AUTHOR]

Summary: This paper is concerned with the formulation of N$$ N $$‐mixture models for estimating the abundance and probability of detection of a species from binary response, count and time‐to‐detection data. A modelling framework, which encompasses time‐to‐first‐detection within the context of detection/non‐detection and time‐to‐each‐detection and time‐to‐first‐detection within the context of count data, is introduced. Two observation processes which depend on whether or not double counting is assumed to occur are also considered. The main focus of the paper is on the derivation of explicit forms for the likelihoods associated with each of the proposed models. Closed‐form expressions for the likelihoods associated with time‐to‐detection data are new and are developed from the theory of order statistics. A key finding of the study is that, based on the assumption of no double counting, the likelihoods associated with times‐to‐detection together with count data are the product of the likelihood for the counts alone and a term which depends on the detection probability parameter. This result demonstrates that, in this case, recording times‐to‐detection could well improve precision in estimation over recording counts alone. In contrast, for the double counting protocol with exponential arrival times, no information was found to be gained by recording times‐to‐detection in addition to the count data. An R package and an accompanying vignette are also introduced in order to complement the algebraic results and to demonstrate the use of the models in practice. [ABSTRACT FROM AUTHOR]

This paper propose a binomial distribution model based on Bayesian statistics in the field of monitoring artificial radionuclides. A multi time-interval analysis method is adopted to extract the 214Bi–214Po correlated events counts in the 222Rn decay series. Then the model evaluates natural background using the ratio of correlated events counts to total α counts. The Beta distribution is used as the prior distribution of this model. We detailed discussed the process of posterior estimation, and compared the new approach with the conventional approaches. The results show the new approach has a more sensitive response to artificial radionuclides. [ABSTRACT FROM AUTHOR]

In this paper, a new threshold INAR(1) model based on modified negative binomial operator with random coefficient is proposed. Basic probabilistic and statistical properties of this process are established. Then the conditional least squares (CLS) and the conditional maximum likelihood (CML) methods are applied to estimate the model parameters when the threshold value is known or not. The asymptotic properties of the CLS-estimator and the CML-estimator are also been discussed. A method to test the constancy of the autoregressive parameters is provided. As an illustration, a simulation study is conducted to illustrate the performances of these estimators and present an empirical analysis of monthly counts of break and enter non-dwelling in Bellingen. [ABSTRACT FROM AUTHOR]

Combinatorial proofs of binomial identities involve establishing an identity by arguing that each side enumerates a certain set of outcomes. In this paper, we share results from interviews with experienced provers (mathematicians and upper-division undergraduate mathematics students) and examine one particular aspect of combinatorial proof, namely the kinds of contexts that experienced provers used to establish combinatorial proofs of binomial identities. Our findings show that overall, our participants used a variety of contexts in their work; we also demonstrate ways in which previous experiences influenced the contexts they chose, and we offer some instances in which features of a context supported their combinatorial proof production. We offer some theoretical implications of our work, and we conclude with a discussion of limitations and avenues for future work. [ABSTRACT FROM AUTHOR]

Summary: The binomial proportion is a classic parameter with many applications and has also been extensively studied in the literature. By contrast, the reciprocal of the binomial proportion, or the inverse proportion, is often overlooked, even though it also plays an important role in various fields. To estimate the inverse proportion, the maximum likelihood method fails to yield a valid estimate when there is no successful event in the Bernoulli trials. To overcome this zero‐event problem, several methods have been introduced in the previous literature. Yet to the best of our knowledge, there is little work on a theoretical comparison of the existing estimators. In this paper, we first review some commonly used estimators for the inverse proportion, study their asymptotic properties, and then develop a new estimator that aims to eliminate the estimation bias. We further conduct Monte Carlo simulations to compare the finite sample performance of the existing and new estimators, and also apply them to handle the zero‐event problem in a meta‐analysis of COVID‐19 data for assessing the relative risks of physical distancing on the infection of coronavirus. [ABSTRACT FROM AUTHOR]

In this paper, event-triggered control for uncertain delayed neural networks (DNNs) with actuator saturation against deception attack is discussed. We propose a novel framework into which an event-triggered mechanism (ETM), actuator saturation, system uncertainty, and deception attack are combined. In the framework, the discrete ETM is employed to determine whether the sampled signal should be transmitted to controller so as to save network bandwidth, a random occurrence deception attack model satisfying Bernoulli distribution is introduced to construct the system robust, and actuator saturation is considered due to the actual complex network environment. Based on the framework, we discussed the stochastic stability of a novel delayed neural network model in a closed-loop system. By resorting to the appropriate Lyapunov–Krasovskii functional (LKF), we derive some new sufficient conditions for the stochastically stable of the system and obtain the gain of the system controller using efficient linear matrix inequality (LMI) method. Finally, a numerical example, in the end, demonstrates the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

The shared frailty models are now popular for modelling heterogeneity in survival analysis. It assumes that the same frailty is shared by all individual members within the families. Also, it is believed that all the individuals in the population are susceptible to the event of interest and will eventually experience the event. This may not always be the situation in reality. There may be a certain fraction of the population which is non-susceptible for an event and hence may not experience the event under study. Non-susceptibility is modelled by frailty models with compound frailty distribution. Further, susceptibility may be different for different families. This can be attained by randomizing the parameter of frailty distribution. This paper incorporates both the things, non-susceptibility and different susceptibility for different families by considering compound negative binomial distribution with random probability of susceptibility as frailty distribution. The inferential problem is solved in a Bayesian framework using Markov Chain Monte Carlo methods. The proposed model is then applied to a real-life data set. [ABSTRACT FROM AUTHOR]

The object of research is the method and algorithm of arithmetic addition of binomial numbers generated by binary binomial counting systems. The lack of binomial arithmetic, in particular the operation of adding binary binomial numbers, in a certain way prevents their introduction into information systems and the construction of information and communication technologies based on them for combinatorial optimization, generation of combinatorial objects, data compression and encryption. In the framework of the proposed approach, instead of operating with binomial coefficients, only operations with their upper and lower parameters are carried out. At the same time, the weighting coefficients of binary binomial numbers, which are added to each other, are represented in the form of two-component tuples. Taking this into account, this paper presents an algorithm for binomial arithmetic addition using dynamic arrays. The main idea, which is included in the structure of the algorithm of binomial arithmetic addition based on dynamic arrays, is that the transition from a two-dimensional model of summation to a one-dimensional one is carried out. At the same time, only available, existing binomial coefficients are placed in the dynamic array. Accordingly, the search for binomial coefficients equal to or greater than the quantitative equivalent takes place in much smaller areas. In comparison with the algorithm based on matrix models, this quite significantly reduces the amount of time spent when performing the summation operation, and also reduces the requirements for the amount of memory required for placing two-component tuples of the assembly array. In the course of the research, a several-fold decrease in the number of machine cycles required to search for the necessary elements in the dynamic array was practically confirmed. This leads to an increase in the performance of the presented algorithm of binomial arithmetic addition based on dynamic arrays. In turn, this leads to the acceleration of solving information tasks of combinatorial optimization, generation of combinatorial objects, data compression and encryption, for the solution of which the operation of adding binary binomial numbers is used. [ABSTRACT FROM AUTHOR]

For state estimation of multi-source asynchronous measurement systems with measurement missing phenomena, this paper proposes a distributed sequential inverse covariance intersection (DSICI) fusion algorithm based on conditional Kalman filtering method. It is mainly divided into synchronized state space module, local filtering module and fusion estimation module. The missing measurements occurring in the system are modelled and described by a set of random variables obeying a Bernoulli distribution. The synchronized state space module uses a state iteration method to synchronize the asynchronous measurement system at the moment of measurement update and it ensures the integrity of the measurement information. The local filtering module uses a conditional Kalman filtering algorithm for filter estimation. The reliability of the local filtering results is guaranteed because the local estimator designs a method to interact information with the domain sensors. The fusion estimation module designs a DSICI fusion algorithm with higher accuracy and satisfying consistency, which fuses the filtering results provided by each sensor when the relevant information between multiple sensors is unknown. Simulation examples demonstrate the excellent performance of the proposed algorithm, with a 33% improvement in accuracy over existing algorithms and an iteration time of less than 3 ms. [ABSTRACT FROM AUTHOR]

This paper considers the problem of randomly varying trial lengths of a class of two-dimensional (2D) linear systems represented by Roesser model, and two new iterative learning control (ILC) schemes are proposed. One is a conventional P-type control rule with a modified tracking error; the other is an ILC law with an iteration-average operator. Both learning control schemes are developed by a 2D stochastic variable to describe varying trial lengths. Under the Bernoulli distribution assumption and the initial state conditions, the convergence analysis is performed rigorously in the probability sense. Finally, illustrative examples have been provided to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Sensitive data, such as financial, personal, or classified governmental information, must be protected throughout its cycle. This paper studies the problem of safeguarding transmitted data based on data categorization techniques. This research aims to use a novel routine as a new meta-heuristic to enhance a novel data categorization based-traffic classification technique where private data is classified into multiple confidential levels. As a result, two packets belonging to the same confidentiality level cannot be transmitted through two routers simultaneously, ensuring a high data protection level. Such a problem is determined by a non-deterministic polynomial-time hardness (NP-hard) problem; therefore, a scheduling algorithm is applied to minimize the total transmission time over the two considered routers. To measure the proposed scheme's performance, two types of distribution, uniform and binomial distributions used to generate packets transmission time datasets. The experimental result shows that the most efficient algorithm is the Best-Random Algorithm (BR˜), recording 0.028 s with an average gap of less than 0.001 in 95.1% of cases compared to all proposed algorithms. In addition, BR˜ is compared to the best-proposed algorithm in the literature which is the Modified decreasing Estimated-Transmission Time algorithm (MDETA). The results show that BR˜ is the best one in 100% of cases where MDETA reaches the best results in only 48%. [ABSTRACT FROM AUTHOR]

This paper deals with testing traffic intensity, which is the most important parameter of the M / M / 1 queue system. The Wald-type sequential probability ratio test (SPRT) is performed to determine traffic intensity by taking advantage of the fact that the total number of customers arriving up to the kth service period, including the kth service period, has a negative binomial distribution. Acceptance and rejection limits obtained from the SPRT are arranged as a multiple sampling plan. This plan is applied with a finite Markov chain. Then, the Operating Characteristic (OC) function and the Average Sample Number (ASN) are obtained precisely. Obtaining the standard errors of the sample number compared to the studies on SPRT applications is the novelty brought by this paper. The sequential analysis method based on the finite Markov chain is also applied to a numerical sample. [ABSTRACT FROM AUTHOR]

This paper investigates the outlier-resistant variance-constrained H ∞ state estimation problem for a class of discrete time-varying recurrent neural networks with randomly occurring deception attacks. The randomly occurring deception attacks are modeled by a series of random variables satisfying the Bernoulli distribution with known probability. In addition, the saturation function is introduced to reduce the negative impact from the measurement outliers onto the estimation performance. The objective of this paper is to propose an outlier-resistant finite-horizon state estimation scheme without utilizing the augmentation method such that, in the presence of measurement outliers and randomly occurring deception attacks, some sufficient criteria are obtained ensuring both the desired H ∞ performance index and the error variance boundedness. Finally, a numerical example is used to illustrate the feasibility of the presented outlier-resistant variance-constrained H ∞ state estimation algorithm. [ABSTRACT FROM AUTHOR]

This paper concerns the mixed H∞$$ {H}_{\infty } $$ and passivity‐based filtering problem for networked nonlinear systems with randomly occurring parameter uncertainties, multipath data packet dropouts, time‐varying delay, and quantization effects. The discrete‐time nonlinear plant considered in this paper is modeled as a Takagi–Sugeno fuzzy system with plant rules. The data missing phenomenon is considered in both measurement and performance output signals due to the unreliable nature of communication links. Further, to reduce the network bandwidth utilization, the measurement quantization is also employed for both the outputs before transmitting through the communication channel. Also, additive filter gain fluctuation is taken into account to reflect the imprecision in filter implementation. Stochastic variables obeying the Bernoulli distribution are incorporated in the model description to characterize the random occurrence of parameter uncertainties and data packet dropouts. A set of sufficient conditions assuring the stochastic stability of the filtering error system with mixed H∞$$ {H}_{\infty } $$ and passivity performance is derived according to Lyapunov stability theory. Finally, three numerical examples including mass–spring–damper and tunnel diode circuit model are established to establish the validity of the developed filter design algorithm. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the screen surface parameters of the double deck vibrating screen, in sections, to determine the influence of each part of the screen surface on the screening efficiency of the vibrating screen. Finally, the best screening parameters were calculated to obtain the best screening performance. Design/methodology/approach: In this paper, the discrete element method is used to simulate the process of two-layer subsection screening. Response surface test was used to analyze the influence of various factors and their interactions on screening results. Finally, based on the binomial regression model of screening efficiency, the optimal combination of vibration parameters is calculated. Findings: In the screening process of vibrating screen, due to the different screening environments in each area of the screen surface, the single-layer linear vibrating screen with equal screen surface parameters cannot obtain the best screening performance. Among the single factors, the effect of vibration frequency is the most significant. Originality/value: To address the issue of single layer linear vibrating screens with equal screen surface parameters being unable to maintain optimal screening performance when handling large amounts of materials. This article proposes a double layer vibrating screen with different screen surface grids and screen surface angles to address the problem of low screening performance of traditional single layer linear vibrating screens. [ABSTRACT FROM AUTHOR]

This paper establishes the strong consistency and asymptotic normality of the negative binomial quasi-maximum likelihood estimator (NBQMLE) for a general class of integer-valued time series models whose parameters are periodic time-varying. This class of models is specified via its conditional mean, which is expressed as a periodic parametric function of (infinite) past observations. An illustration on specific models, namely the Poisson periodic INGARCH model, the negative binomial periodic INGARCH model, and the periodic INAR(1) model is given. In addition, the performance of the NBQMLE is assessed through a simulation study, and an application of the proposed methodology to a real dataset is provided. [ABSTRACT FROM AUTHOR]

The standard binomial distribution is based on a sequence of Bernoulli trials. The probability of success is the same for each trial. In the Generalized Binomial Distribution (GBD), the probability of success changes by the history of successes up to that point. For example, if a student correctly answers a large proportion of the first few questions, the probability of correctly answering the next question increases because the history of successes may indicate skill. The Bernoulli events are correlated. Alternatively, the standard binomial distribution does not consider the history of successes, and assumes that successes are not correlated. In this paper we prove some new properties of the GBD and apply the concept to five new areas in sport competition, finance, biology, meteorology, and testing pseudo-random number generators. We prove that the GBD predicts the results in the collected data significantly better than the standard binomial distribution thus proving that the events are indeed correlated. We provide an R code, and a supplementary Excel file that provide users with an easy way to analyze any collected data set based on Bernoulli processes. [ABSTRACT FROM AUTHOR]

Consider a sequence (X n) n ≥ 1 of i.i.d. 2 × 2 stochastic matrices with each X n distributed as μ. This μ is described as follows. Let (C n , D n) T denote the first column of X n and for a given real r with 0 < r < 1 , let r − 1 C n and r − 1 D n each be Bernoulli distributions with parameters p 1 and p 2 , respectively, and 0 < p 1 , p 2 < 1 . Clearly, the weak limit of the sequence μ n , namely λ , is known to exist, whose support is contained in the set of all 2 × 2 rank one stochastic matrices. In a previous paper, we considered 0 < r ≤ 1 2 and obtained λ explicitly. We showed that λ is supported countably on many points, each with positive λ -mass. Of course, the case 0 < r ≤ 1 2 is tractable, but the case r > 1 2 is very challenging. Considering the extreme nontriviality of this case, we stick to a very special such r, namely, r = 5 − 1 2 (the reciprocal of the golden ratio), briefly mention the challenges in this nontrivial case, and completely identify λ for a very special situation. [ABSTRACT FROM AUTHOR]

The multibridgeR package allows a Bayesian evaluation of informed hypotheses H r applied to frequency data from an independent binomial or multinomial distribution. multibridge uses bridge sampling to efficiently compute Bayes factors for the following hypotheses concerning the latent category proportions 휃: (a) hypotheses that postulate equality constraints (e.g., 휃1 = 휃2 = 휃3); (b) hypotheses that postulate inequality constraints (e.g., 휃1 < 휃2 < 휃3 or 휃1 > 휃2 > 휃3); (c) hypotheses that postulate combinations of inequality constraints and equality constraints (e.g., 휃1 < 휃2 = 휃3); and (d) hypotheses that postulate combinations of (a)–(c) (e.g., 휃1 < (휃2 = 휃3),휃4). Any informed hypothesis H r may be compared against the encompassing hypothesis H e that all category proportions vary freely, or against the null hypothesis H 0 that all category proportions are equal. multibridge facilitates the fast and accurate comparison of large models with many constraints and models for which relatively little posterior mass falls in the restricted parameter space. This paper describes the underlying methodology and illustrates the use of multibridge through fully reproducible examples. [ABSTRACT FROM AUTHOR]

This paper is concerned with the input–output finite-time (IO-FT) stabilisation problem for a class of continuous-time periodic piecewise polynomial systems (PPPSs) with immeasurable states and external disturbances via state estimation-based robust reliable controller. Firstly, to reflect the actuality, a parameter uncertainty that exhibits the random nature and the actuator faults with nonlinear character are considered in the addressed PPPSs and the control scheme, respectively. In detail, the randomness of uncertain parameters is portrayed by the stochastic variable and it is presumed to pursue the Bernoulli distributions. Secondly, to estimate the immeasurable states of PPPSs, a periodic piecewise polynomial observer is designed depending on the output of PPPSs. The main intent of this article is to devise a state estimation-based robust reliable controller to ascertain the IO-FT stabilisation of the PPPSs. Moreover, by bridging the Lyapunov stability theory, linear matrix inequality technique and IO-FT stability theory, the required IO-FT stabilisation conditions in the frame of linear matrix inequality are procured for the system under consideration. Eventually, simulation results of the addressed PPPSs are shown in line with the proposed analytical findings, revealing the competence, inherent capability and utility of the devised control protocol. [ABSTRACT FROM AUTHOR]

This paper is devoted to a new two‐parameter distribution on ℤ having an original additive stochastic structure. It is defined by the sum of two independent discrete random variables, where one is defined based on the Laplace distribution and the other on a transformed version of a distribution that can be viewed as a relative binomial distribution. It can thus also be viewed as a perturbed version of the Laplace distribution. We present some interesting properties of the proposed distribution, such as its moments (ordinary, non‐central, incomplete moments, etc.), characteristic function, skewness, and kurtosis, among others. The distribution is also applied to practical datasets from finance and health studies, where it is seen to perform better than some of the existing models defined on ℤ. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of periodic negative binomial integer-valued generalized autoregressive conditional heteroskedastic model. The basic probabilistic and statistical properties of this class are studied. Indeed, the first and the second moment periodically stationary conditions are established. The closed-forms of these moments are, under the obtained conditions, derived. Furthermore, the condition for the existence of higher moment orders and their explicit formula in terms of the parameters are established. The periodic autocovariance structure is also considered while providing the closed-form of the periodic autocorrelation function. The Yule-Walker (YW), the conditional least squares (CLS), and the conditional maximum likelihood (CML) methods are applied to estimate the underlying parameters. The performances of these methods are compared through a simulation study. An application to a real data set is provided. [ABSTRACT FROM AUTHOR]

In this paper, we study a new type of distribution that generalizes distributions from the gamma and beta classes that are widely used in applications. The estimators for the parameters of the digamma distribution obtained by the method of logarithmic cumulants are considered. Based on the previously proved asymptotic normality of the estimators for the characteristic index and the shape and scale parameters of the digamma distribution constructed from a fixed-size sample, we obtain a statement about the convergence of these estimators to the scale mixtures of the normal law in the case of a random sample size. Using this result, asymptotic confidence intervals for the estimated parameters are constructed. A number of examples of the limit laws for sample sizes with special forms of negative binomial distributions are given. The results of this paper can be widely used in the study of probabilistic models based on continuous distributions with an unbounded non-negative support. [ABSTRACT FROM AUTHOR]

Although logistic regression is the most popular for modelling regression relationships with binary responses, many find relative risk (RR), or risk ratio, easier to interpret and prefer to use this measure of risk in regression analysis. Indeed, since Zou published his modified Poisson regression approach for modelling RR for cross-sectional data, his paper has been cited over 7 000 times, demonstrating the popularity of this alternative measure of risk in regression analysis involving binary responses. As longitudinal studies have become increasingly popular in clinical trials and observational studies, it is imperative to extend Zou's approach for longitudinal data. The two most popular approaches for longitudinal data analysis are the generalised linear mixed-effects model (GLMM) and generalised estimating equations (GEE). However, the parametric GLMM cannot be used for the extension within the current context, because Zou's approach treats the binary response as a Poisson variable, which is at odds with the Bernoulli distribution for the binary response. On the other hand, as it imposes no mathematical model on data distributions, the semiparametric GEE is coherent with Zou's modified Poisson regression. In this paper, we develop a GEE-based longitudinal model for binary responses to provide inference about RR. [ABSTRACT FROM AUTHOR]

The Sombor indices, a new category of degree-based topological molecular descriptors, have been widely investigated due to their excellent chemical applicability. This paper aims to establish Sombor index distributions in random polygonal chain networks and to derive expressions for their expected values and variances. The expected values and variances of the Sombor indices for polyonino, pentachain, polyphenyl, and cyclooctane chains are obtained. Since the end connection of a random chain network follows a binomial distribution, the Sombor indices of any chain network follow a normal distribution as the number of polygons connected by the chain (indicated by n) approaches infinity. [ABSTRACT FROM AUTHOR]

Human activity recognition (HAR) is one of the key applications of health monitoring that requires continuous use of wearable devices to track daily activities. The most efficient supervised machine learning (ML)-based approaches for predicting human activity are based on a continuous stream of sensor data. Sensor data analysis for human activity recognition using conventional algorithms and deep learning (DL) models shows promising results, but evaluating their ambiguity in decision-making is still challenging. In order to solve these issues, the paper proposes a novel Wasserstein gradient flow legonet WGF-LN-based human activity recognition system. At first, the input data is pre-processed. From the pre-processed data, the features are extracted using Haar Wavelet mother- Symlet wavelet coefficient scattering feature extraction (HS-WSFE). After that, the interest features are selected from the extracted features using (Binomial Distribution integrated-Golden Eagle Optimization) BD-GEO. The important features are then post-processed using the scatter plot matrix method. Obtained post-processing features are finally given into the WGF-LN for classifying human activities. From these experiments, the results can be obtained and showed the efficacy of the proposed model. [ABSTRACT FROM AUTHOR]

Acceptance sampling plans (ASPs) are conducted by inspecting a small set of items instead of all outputs. Although traditional ASPs use certain plan parameters, it is clear that quality characteristics or definitions may not be certain in some real case applications because of uncertainties. The fuzzy set theory (FST) is a popular technique to model uncertainty in the engineering problems. It is known that ASPs have been successfully formulated based on FST in the literature. However, the uncertainty is generally more complex in cases including human evaluations. Neutrosophic sets (NSs) that is one of the fuzzy set extensions bring some advantages to manage more complicated uncertainties in quality problems especially uncertainty based on human's hesitancy. Since the NSs include three terms as truthiness (t), indeterminacy (i), and falsity (f), they can successfully model the human thinking and inspectors' evaluations under uncertainty. In this paper, traditional attribute ASPs have been extended based on interval NSs to combine the computational and interpretational advantages of the interval statistics with the advantages of NSs. Additionally, two well-known distributions for ASPs called Binomial and Poisson distributions are redesigned by using NSs. For this aim, NSs are converted to interval NSs by using α-cut technique and some characteristic functions of ASPs such as acceptance probability ( P a ), average sample number ( ASN ), and average total inspection ( ATI ) have been designed for single and double ASPs based on interval NSs. The proposed ASPs based on NSs have been tested on some numerical applications from a manufacturing process, and results obtained based on real cases have been compared. [ABSTRACT FROM AUTHOR]

This paper introduces two novel subclasses of the function class Σ for bi-univalent functions, leveraging generalized telephone numbers and Binomial series through convolution. The exploration is conducted within the domain of the open unit disk. We delve into the analysis of initial Taylor-Maclaurin coefficients | a 2 | and | a 3 | , deriving insights and findings for functions belonging to these new subclasses. Additionally, Fekete-Szegö inequalities are established for these functions. Furthermore, the study unveils a range of new subclasses of Σ , some of which are special cases, yet have not been previously explored in conjunction with telephone numbers. These subclasses emerge as a result of hybrid-type convolution operators. Concluding from our results, we present several corollaries, which stand as fresh contributions in the domain of involution numbers involving hybrid-type convolution operators. [ABSTRACT FROM AUTHOR]

In this paper, we prove a local limit theorem and a refined continuity correction for the negative binomial distribution. We present two applications of the results. First, we find the asymptotics of the median for a NegativeBinomial (r , p) random variable jittered by a Uniform (0 , 1) , which answers a problem left open in Coeurjolly and Trépanier (Metrika 83(7):837–851, 2020). This is used to construct a simple, robust and consistent estimator of the parameter p, when r > 0 is known. The case where r is unknown is also briefly covered. Second, we find an upper bound on the Le Cam distance between negative binomial and normal experiments. [ABSTRACT FROM AUTHOR]

Rating data are a kind of ordinal categorical data routinely collected in survey sampling. The response value in such applications is confined to a finite number of ordered categories. Due to population heterogeneity, the respondents may have several different rating styles. A finite mixture model is thus most suitable to fit datasets of this nature. In this paper, we propose a two-component mixture of shifted binomial distributions for rating data. We show that this model is identifiable and propose a numerically stable penalized likelihood approach for parameter estimation. We adapt an expectation-maximization algorithm for the penalized maximum likelihood estimation. Our simulation results show that the penalized maximum likelihood estimator is consistent and effective. We fit the proposed model and other models in the literature to some real-world datasets and find the proposed model can have much better fits. [ABSTRACT FROM AUTHOR]

In this paper, we tackle the problem of the intensity attenuation at Ischia, a critical parameter in a high seismic risk area such as this volcanic island. Starting from the new revised catalogue of local earthquakes, we select a dataset of 118 macroseismic observations related to the four main historical events and analyse the characteristics of the intensity attenuation according to both the deterministic and probabilistic approaches, under the assumption of a point seismic source and isotropic decay (circular spreading). In the deterministic analysis, we derive the attenuation law through an empirical model fitting the average values of ΔI (the difference between epicentral intensity I0 and intensities observed at a site IS) versus the epicentral distances by the least-square method. In the probabilistic approach, the distribution of IS conditioned on the epicentre-site distance is given through a binomial-beta model for each class of I0. In the Bayesian framework, the model parameter p is considered as a random variable to which we assign a Beta probability distribution on the basis of our prior belief derived from investigations on the attenuation in Italy. The mode of the binomial distribution is taken as the intensity expected at that site (Iexp). The entire calculation procedure has been implemented in a python plugin for QGIS® software that, given location and I0 (or magnitude) of the earthquake to be simulated, generates a probabilistic seismic scenario according to the deterministic or probabilistic models of attenuation. This tool may be applied in seismic risk analyses at a local scale or in the seismic surveillance to produce real-time intensity shake-maps for this volcanic area. [ABSTRACT FROM AUTHOR]

The continuous Bernoulli distribution is a one-parameter probability distribution which is useful in analysis on machine learning. A handful of studies has been done to generalize the continuous Bernoulli distribution. In this paper, we introduced a wider extension of the continuous Bernoulli distribution by considering its distribution function as a generator. We referred to the proposed family as the continuous Bernoulli-generated family of distributions. Basic statistical treatments of the proposed family such as the density and cumulative distribution functions, survival and hazard rate functions, quantile, moments, moment generating function, and Renyi entropy are derived. The method of maximum likelihood is employed to estimate the unknown parameters of the family and the asymptotic behaviour of the parameter estimates is investigated via Monte Carlo simulation study. The waiting time (in minutes) of 100 Bank customers and the tensile strength measured in GPa, of 69 carbon fibers data sets formed the basis for real-life data fittings. Results obtained from the fitting of the two data sets when compared with some existing non-nested models revealed that the fittings were in favor of the continuous-Bernoulli Weibull distribution over the rest competing distributions. [ABSTRACT FROM AUTHOR]

The use of the lambda-mu-sigma (LMS) method for estimating centiles and producing reference ranges has received much interest in clinical practice, especially for assessing growth in childhood. However, this method may not be directly applicable where measures are based on a score calculated from question response categories that is bounded within finite intervals, for example, in psychometrics. In such cases, the main assumption of normality of the conditional distribution of the transformed response measurement is violated due to the presence of ceiling (and floor) effects, leading to biased fitted centiles when derived using the common LMS method. This paper describes the methodology for constructing reference intervals when the response variable is bounded and explores different distribution families for the centile estimation, using a score derived from a parent-completed assessment of cognitive and language development in 24 month-old children. Results indicated that the z-scores, and thus the extracted centiles, improved when kurtosis was also modeled and that the ceiling effect was addressed with the use of the inflated binomial distribution. Therefore, the selection of the appropriate distribution when constructing centile curves is crucial. [ABSTRACT FROM AUTHOR]

Attribute control charts assuming a Poisson (c chart) or a binomial distribution (np chart) are usually used when the quality characteristic cannot be measured on a continuous scale. For equivalent sample sizes, Shewhart type attribute control charts are known to be less efficient than their measurement counterparts (like the X ¯ chart) and, for this reason, practitioners often compensate it by supplementing them with an EWMA (Exponentially Weighted Moving Average) scheme. However, because of the discrete nature of count data, it is unfortunately impossible to compute exactly and accurately (by means of Markov chain of integral equation methods) the run length (RL) properties, such as its mean (ARL) and its standard deviation (SDRL) of these EWMA attribute control charts and, consequently, it is impossible to efficiently design them in order to minimize some out-of-control characteristics. For this reason, we propose in this paper a dedicated approach called "continuousify" method which, coupled with a classical Markov chain technique, allows to compute the RL properties of any EWMA attribute control chart in a reliable way. A numerical comparison shows that the RL properties obtained by using the proposed "continuousify" approach are very much alike to the ones calculated via simulation and without the "continuousify" approach. Illustrative examples are also provided to show how the proposed method can be implemented in practice. [ABSTRACT FROM AUTHOR]

In this paper, we present the exact distribution of the sum of two independent Topp-Leone variables which becomes useful in calculating the exact reliability of a standby system with Topp-Leone distributed component units when the values of parameters are known. Applications in Bayesian analysis with binomial sampling are also considered, and the comparison of the performance of Beta and Topp-Leone priors is then made. [ABSTRACT FROM AUTHOR]

The Median-of-Mean (MoM) estimation is an efficient statistical method for handling data with contamination. In this paper, we propose a variance-dependent MoM estimation method using the tail probability of a binomial distribution. The bound of this method is better than the classical Hoeffding method under mild conditions. This method is then used to study the concentration of variance-dependent MoM empirical processes and sub-Gaussian intrinsic moment norm. Finally, we give the bound of the variance-dependent MoM estimator with distribution-free contaminated data. [ABSTRACT FROM AUTHOR]

Process capability and performance indices (PCIs and PPIs) are used in industry to provide numerical measures for the capability and performance of several processes. The majority of the literature refers to PCIs and PPIs for continuous data. The aim of this paper is to compute the classical indices for discrete data following Poisson, binomial or negative binomial distribution using various transformation techniques. A simulation study under different situations of a process and comparisons with other existing PCIs for discrete data are also presented. The methodology of computing the indices is easy to use, and as a result, one can have an assessment of the process capability and performance without difficulty. Three examples are further provided to illustrate the application of the transformation techniques. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new kind of conformable stochastic impulsive differential systems (CSIDS) involving discrete distribution of Bernoulli. For random discontinuous trajectories, we modify the tracking error of piecewise continuous variables by a zero-order holder. First, the improved P-type and PDα-type learning laws of the random iterative learning control (ILC) scheme are designed through global and local averaging operators. Next, we establish sufficient conditions for convergence of the tracking error in the expectation sense and prove the main results by using the impulsive Gronwall inequality and mathematical analysis tools. Finally, the theoretical results are verified by two numerical examples, and the tracking performance is compared for different conformable order of α. [ABSTRACT FROM AUTHOR]

Summary: This paper investigates a scalable recursive state estimation method for nonlinear two‐dimensional (2‐D) stochastic complex networks. In these networks, the switching topology is modelled by random variables generated by the Bernoulli distribution. Considering the Extended Kalman Filter structure, we employ the Taylor series expansion to handle the nonlinear functions in the model. Hence, high‐order terms emerging in the linearization process are modelled by norm‐bounded parameter uncertainties. Due to the uncertainty of such a system, we obtain an upper bound for the estimation error covariance. Furthermore, we obtain an upper bound for the cross covariance to reduce the proposed filter's computational complexity and improve scalability. Within the established setting, next, the proposed filter is designed in such a way that the presented upper bounds are minimized. Finally, a numerical example is provided to illustrate the effectiveness of the proposed state estimation algorithm. [ABSTRACT FROM AUTHOR]

This paper investigates an observer-based state estimation issue for discrete-time semi-Markovian jump neural networks with Round-Robin protocol and cyber attacks. In order to avoid the network congestion and save the communication resources, the Round-Robin protocol is used to schedule the data transmissions over the networks. Specifically, the cyber attacks are modeled as a set of random variables satisfying the Bernoulli distribution. On the basis of the Lyapunov functional and the discrete Wirtinger-based inequality technique, some sufficient conditions are established to guarantee the dissipativity performance and mean square exponential stability of the argument system. In order to compute the estimator gain parameters, a linear matrix inequality approach is utilized. Finally, two illustrative examples are provided to demonstrate the effectiveness of the proposed state estimation algorithm. [ABSTRACT FROM AUTHOR]

In this paper, the stochastic sampled-data exponential synchronization problem for Markovian jump neural networks (MJNNs) with time-varying delays and the reachable set estimation (RSE) problem for MJNNs subjected to external disturbances are investigated. Firstly, assuming that two sampled-data periods satisfy Bernoulli distribution, and introducing two stochastic variables to represent the unknown input delay and the sampled-data period respectively, the mode-dependent two-sided loop-based Lyapunov functional (TSLBLF) is constructed, and the conditions for the mean square exponential stability of the error system are derived. Furthermore, a mode-dependent stochastic sampled-data controller is designed. Secondly, by analyzing the unit-energy bounded disturbance of MJNNs, a sufficient condition is proved that all states of MJNNs are confined to an ellipsoid under zero initial condition. In order to make the target ellipsoid contain the reachable set of the system, a stochastic sampled-data controller with RSE is designed. Eventually, two numerical examples and an analog resistor–capacitor network circuit are provided to show that the textual approach can obtain a larger sampled-data period than the existing approach. [ABSTRACT FROM AUTHOR]

In this paper, we established an effective formula for Dnestrovskii functions based on the binomial expansion theorem which frequently appears in a weakly relativistic loss cone distribution, relativistic, magnetized, and thermal plasmas. The obtained formulas are expressed in terms of binomial coefficients and incomplete Gamma functions. Therefore, the proposed approach is a fully useful method to evaluate Dnestrovskii functions and related physical properties of plasmas. Calculation results of the Dnestrovskii functions are compared with other numerical and theoretical models and indicated acceptable agreement. The results of the calculations demonstrate that the derived formula is valid for a wide range of parameters. [ABSTRACT FROM AUTHOR]

Comparative Poisson trials of an experimental treatment versus a control typically condition on the total number of events that occur across both arms (Design A). Inference is based on the binomial distribution. Recently, an approach termed Design C to compare K experimental treatments to the same control was introduced. Under Design C without curtailment, the trial continues until a prespecified number of events occur in the control arm, leading to inference based on the negative multinomial distribution. The question remains of how advantageous it is to conduct one Design C trial comparing K experimental treatment arms to the same control arm as opposed to conducting K separate Design A trials each comparing one experimental treatment arm to a different control arm. This paper, therefore, compares the expected number of subjects to enroll for the two designs under uncurtailed and curtailed settings. The designs are evaluated when the null hypothesis and various assumptions for the alternative hypothesis hold. We simulate a variety of combinations for the Type 1 error, power, and ratio of the incidence rate of events in the experimental treatment to control arms. Design C frequently offers significant savings in terms of sample size relative to Design A. [ABSTRACT FROM AUTHOR]

Purpose: This paper aims to explore the realm of literature about personalization of digital library services. This paper focuses on users' unique needs and will identify different types of personalized services. Therefore, this study has identified different types of services personalization in the context of digital academic libraries. Design/methodology/approach: In this research, the systematic review method has been used to obtain the relevant indicators of different types of personalization in the context of libraries. To explain basic indicators, a Delphi method has been used. The Delphi panel's members consisted of 15 experts (faculty members, researchers, professional users and software designers). A purposeful sampling and the Delphi fulfillment process were performed in three rounds. After collecting data, descriptive statistics (mean and standard deviation), inferential statistics (binomial distribution test) and the Kendall coordination coefficient were used to determine the consensus rate among experts. Findings: A total of 103 indicators were extracted for different types of personalization through a systematic literature review. Of these, 90 indicators were considered significant in the experts' view. Generally, content personalization, interactive personalization, collaborative personalization and information retrieval personalization are the main components of personalization types, each of which has its own indicators. Originality/value: This study has dealt with the issue of what is personalized in the context of digital academic library. The findings should be helpful and effective in the development of a holistic view on personalization of services in digital libraries. [ABSTRACT FROM AUTHOR]

In this paper, an underwater robot system with nonlinear characteristics is studied by a backstepping method. Based on the state preservation problem of an Autonomous Underwater Vehicle (AUV), this paper applies the backstepping probabilistic gain controller to the nonlinear system of the AUV for the first time. Under the comprehensive influence of underwater resistance, turbulence, and driving force, the motion of the AUV has strong coupling, strong nonlinearity, and an unpredictable state. At this time, the system's output feedback can solve the problem of an unmeasurable state. In order to achieve a good control effect and extend the cruising range of the AUV, first, this paper will select the state error to make it a new control objective. The system's control is transformed into the selection of system parameters, which greatly simplifies the degree of calculation. Second, this paper introduces the concept of a stochastic backstepping control strategy, in which the robot's actuators work discontinuously. The actuator works only when there is a random disturbance, and the control effect is not diminished. Finally, the backstepping probabilistic gain controller is designed according to the nonlinear system applied to the simulation model for verification, and the final result confirms the effect of the controller design. [ABSTRACT FROM AUTHOR]

This paper is concerned with the problem of finite-time synchronization for a class of discrete-time semi-Markovian jumping complex dynamical networks (CDNs) with actuator faults based on reliable control. The main aim of this paper is to design a state feedback controller such that the resulting closed-loop system is finite-time synchronized under a prescribed dissipativity performance level even in the presence of actuator failures. Moreover, a stochastic nature followed by Bernoulli distribution is described in the considered networks due to the occurrence of probabilistic nature in time-varying delays. By composing a suitable Lyapunov–Krasovskii functional containing triple summation terms with the aid of Kronecker product properties, Lyapunov stability theory and free weighting matrix approach, sufficient criteria are established in terms of linear matrix inequalities that assure finite-time synchronization and meet the dissipativity performance to the addressed CDNs. The usefulness of the presented design scheme is finally verified by numerical examples. [ABSTRACT FROM AUTHOR]