A class of bivariate integer-valued time series models was constructed via copula theory. Each series follows a Markov chain with the serial dependence captured using copula-based transition probabilities from the Poisson and the zero-inflated Poisson (ZIP) margins. The copula theory was also used again to capture the dependence between the two series using either the bivariate Gaussian or “t-copula” functions. Such a method provides a flexible dependence structure that allows for positive and negative correlation, as well. In addition, the use of a copula permits applying different margins with a complicated structure such as the ZIP distribution. Likelihood-based inference was used to estimate the models’ parameters with the bivariate integrals of the Gaussian or t-copula functions being evaluated using standard randomized Monte Carlo methods. To evaluate the proposed class of models, a comprehensive simulated study was conducted. Then, two sets of real-life examples were analyzed assuming the Poisson and the ZIP marginals, respectively. The results showed the superiority of the proposed class of models.

One of the important features of generalized distribution is its ability and flexibility to model real-life data in several applied fields such as medicine, engineering, and survival analysis, among others. In this paper, a flexible four-parameter Lomax extension called the alpha-power power-Lomax (APPLx) distribution is introduced. The APPLx distribution is analytically tractable, and it can be used quite effectively for real-life data analysis. Key mathematical properties of the APPLx distribution including mode, moments, stress-strength reliability, quantile and generating functions, and order statistics are presented. The APPEx parameters are estimated by using eight classical estimation methods. Extensive simulation studies are provided to explore the performance of the proposed estimation methods and to provide a guideline for practitioners and engineers to choose the best estimation method. Three real-life datasets from applied fields are fitted to assess empirically the flexibility of the APPLx distribution. The APPLx distribution shows greater flexibility as compared to the McDonal–Lomax, Fréchet Topp–Leone Lomax, transmuted Weibull–Lomax, Kumaraswamy–Lomax, beta exponentiated-Lomax, Weibull–Lomax, Burr-X Lomax, Lomax–Weibull, odd exponentiated half-logistic Lomax, and alpha-power Lomax distributions.

The exponential distribution is one of the most widely used statistical distribution for reliability issues. In this paper, we introduce a novel family based on the exponential model, called the new exponential-H (NEx-H) family. The sub-models of the NEx-H family are capable of accommodating variable failure rates, as well as unimodal, bimodal, left-skewed, symmetric, right-skewed, and J-shape densities. The mathematical features of the NEx-H family are derived. The parameters of the NEx-Weibull distribution are estimated by using seven estimation methods. Detailed numerical simulations are presented. Based on our study, the maximum likelihood is the best estimation method for estimating the NEx-Weibull parameters. Three real-life data sets are fitted using the NEx-Weibull distribution. The NEx-Weibull model provides better fit as compared to some competing Weibull models.

Discrete choice models (DCMs) are applied in statistical modelling of consumer behavior. Such models are used in many areas including social sciences, health economics, transportation research, and health systems research and they are time dependent. In this manuscript, we review references on the study of such models, develop DCMs with emphasis on time dependent best-worst choice and discrimination between choice attributes. Referenced measurements of the dynamic DCMs are simulated. Expected utilities over time are derived using Markov decision processes. We study attributes and attribute-levels associated with the quality of life of seniors, report the estimation results, and discuss our findings.

Time series analysis is crucial for modeling and forecasting diverse real-world phenomena. Traditional models typically assume continuous-valued data; however, many applications involve integer-valued series, often including negative integers. This paper introduces an approach that combines copula theory with the bivariate Skellam distribution to handle such integer-valued data effectively. Copulas are widely recognized for capturing complex dependencies among variables. By integrating copulas, our proposed method respects integer constraints while modeling positive, negative, and temporal dependencies accurately. Through simulation and an empirical study on a real-life example, we demonstrate that our class of models performs well. This approach has broad applicability in areas such as finance, epidemiology, and environmental science, where modeling series with integer values, both positive and negative, is essential.