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This manuscript presents a new two-parameter unit stochastic distribution, obtained by transforming the Laplace distribution, using a generalized logistic map, into a unit interval. The distribution thus obtained is named the Laplace-logistic unit (abbreviated LLU) distribution, and its basic stochastic properties are examined in detail. Also, the procedure for estimating parameters based on quantiles is provided, along with the asymptotic properties of the obtained estimates and the appropriate numerical simulation study. Finally, the application of the LLU distribution in dynamic and regression analysis of real-world data with accentuated “peaks” and “fat” tails is also discussed.

The manuscript deals with a new unit distribution that depends on two positive parameters. The distribution itself was obtained from the Gumbel distribution, i.e., by its transformation, using generalized logistic mapping, into a unit interval. In this way, the so-called Gumbel-logistic unit (abbr. GLU) distribution is obtained, and its key properties, such as cumulative distribution function, modality, hazard and quantile function, moment-based characteristics, Bayesian inferences and entropy, have been investigated in detail. Among others, it is shown that the GLU distribution, unlike the Gumbel one which is always positively asymmetric, can take both asymmetric forms. An estimation of the parameters of the GLU distribution, based on its quantiles, is also performed, together with asymptotic properties of the estimates thus obtained and their numerical simulation. Finally, the GLU distribution has been applied in modeling the empirical distributions of some real-world data related to telecommunications.

Zero-and-one inflated count time series have only recently become the subject of more extensive interest and research. One of the possible approaches is represented by first-order, non-negative, integer-valued autoregressive processes with zero-and-one inflated innovations, abbr. ZOINAR(1) processes, introduced recently, around the year 2020 to the present. This manuscript presents a generalization of ZOINAR processes, given by introducing the zero-and-one inflated power series (ZOIPS) distributions. Thus, the obtained process, named the ZOIPS-INAR(1) process, has been investigated in terms of its basic stochastic properties (e.g., moments, correlation structure and distributional properties). To estimate the parameters of the ZOIPS-INAR(1) model, in addition to the conditional least-squares (CLS) method, a recent estimation technique based on probability-generating functions (PGFs) is discussed. The asymptotic properties of the obtained estimators are also examined, as well as their Monte Carlo simulation study. Finally, as an application of the ZOIPS-INAR(1) model, a dynamic analysis of the number of deaths from the disease COVID-19 in Serbia is considered.

In this manuscript, a new two-parameter stochastic distribution is proposed and obtained by a continuous half-logistic transformation of the quasi-Lindley (QL) distribution to the unit interval. The resulting distribution, named the quasi-Lindley half-logistic unit (QHU) distribution, is examined in terms of its key stochastic properties, such as asymmetry conditions, shape and modality, moments, etc. In addition, the stochastic dominance of the proposed distribution with respect to its parameters is considered, and it is shown that the QHU distribution, in contrast to the QL distribution that is always positively asymmetric, can have both asymmetric forms. The parameters of the QHU distribution are estimated by the maximum likelihood (ML) method, and the asymptotic properties of thusly obtained estimators are examined. Finally, an application of the proposed distribution in modeling some real-world phenomena is also presented.

This manuscript deals with a novel, nonlinear, and non-stationary stochastic model with symmetric, Laplacian distributed innovations. The obtained model, named Laplacian Split-BREAK (LSB) process, is intended for dynamic analysis of time series with pronounced and permanent fluctuations. By using the method of characteristic functions (CFs), the basic stochastic properties of the LSB process are proven, with a special emphasis on its asymptotic behaviour. The different procedures for estimating its parameters are also given, along with numerical simulations of the obtained estimators. Finally, it has been shown that the LSB process, as an adequate stochastic model, can be applied in the analysis of dynamics in the world market of crude oil and natural gas.

This paper introduces the Poisson-Lindley minification integer-valued autoregressive (PL-MINAR) process, a novel statistical model for analyzing count time series data. The modified negative binomial thinning and the Poisson-Lindley (PL) marginal distribution served as the foundation for the model. The proposed model was examined in terms of its basic stochastic properties, especially related to conditional stochastic measures (e.g., transition probabilities, conditional mean and variance, autocorrelation function). Through comprehensive simulations, the effectiveness of various parameter estimation techniques was validated. The PL-MINAR model's practical utility was demonstrated in analyzing the number of Bitcoin transactions and stock trades, showing its superior or comparable performance to the established INAR model. By offering a robust tool for financial time series analysis, this research holds potential for significant improvements in forecasting and understanding market dynamics.

Motivated by certain problems connected with the stochastic analysis of the recursively defined time series, in this paper, we define and study some polynomial sequences. Beside computation of these polynomials and their connection to the Euler–Apostol numbers, we prove some basic properties and give an interesting connection of these polynomials with the well-known Bernoulli numbers, as well as some new summation formulas for Bernoulli’s numbers. Finally, we prove that zeros of these polynomials are simple, real and symmetrically distributed in [0,1].

Distributions with bounded support show considerable sparsity over those with unbounded support, despite the fact that there are a number of real-world contexts where observations take values from a bounded range (proportions, percentages, and fractions are typical examples). For proportion modeling, a flexible family of two-parameter distribution functions associated with the exponential distribution is proposed here. The mathematical and statistical properties of the novel distribution are examined, including the quantiles, mode, moments, hazard rate function, and its characterization. The parameter estimation procedure using the maximum likelihood method is carried out, and applications to environmental and engineering data are also considered. To this end, various statistical tests are used, along with some other information criterion indicators to determine how well the model fits the data. The proposed model is found to be the most efficient plan in most cases for the datasets considered.

The manuscript examines the cause-and-effect relationships of fires in the Republic of Serbia over a fifteen-year period, primarily from the aspect of human safety. For this purpose, numerical variables describing the number of injuries and deaths in fires were introduced, on which various analysis and modeling techniques were implemented, which can be viewed in the context of data mining (DM). First, for both observed variables, stochastic modeling of their temporal dynamics was analyzed, and subsequently, cluster analysis of the values of these variables was performed using two different methods. Finally, by interpreting these variables as outputs (objectives) for the classification problem, several decision trees were formed that describe the influence and relationship of different fire causes on situations in which injuries or human casualties occur or not. In that way, several different types of fires have been identified, including rare but deadly incidents that require urgent preventive measures. Key risk factors such as fire cause, location, season, etc., have been found to significantly influence human casualties. These findings provide practical insights for improving fire protection policies and emergency response. Through such a comprehensive analysis, it is believed that some important results have been obtained that precisely describe the specific relationships between the causes and consequences of fires occurring in the Republic of Serbia.

The manuscript proposes a new non-linear and non-stationary bivariate stochastic model, termed the two-dimensional Gaussian (generalized) Split-BREAK (2D-GSB) process, as a multivariate extension of the univariate GSB framework. The generalization consists in introducing a common threshold mechanism based on the norm of a bivariate innovation vector and a single synchronized Bernoulli indicator which jointly governs regime activation in both components. This structure induces cross-dependent regime shifts and yields a binomial–Gaussian mixture representation of the joint distribution, explicitly linking contemporaneous dependence with a common latent regime mechanism. The fundamental properties of the proposed model are established, with particular emphasis on its asymptotic behavior. Parameter estimation procedure is developed using both the method of moments (MoM) and the empirical characteristic function (ECF) approach, and their performance is evaluated through Monte Carlo simulations. An empirical application to daily crime data illustrates how the proposed framework captures synchronized structural shocks and heavy-tailed features in related crime categories. In comparison with a standard VAR(1) benchmark, the 2D-GSB specification provides a parsimonious yet substantially improved likelihood-based fit, thus offering a theoretically sound framework for analyzing multivariate time series characterized by synchronized regime shifts and heavy-tailed behavior.