Abstract
Sales forecasting is very important in retail management. It helps with decisions about inventory, staffing, and planning promotions. In this study, we looked at how to balance the accuracy of predictions with how easy it is to understand the machine learning models used in sales forecasting. We used public data from Rossmann stores to study various factors like promotions, holidays, and store features that affect daily sales. We compared a complex, highly accurate model (XGBoost) with simpler, easier-to-understand linear regression models. To find a middle ground, we created a hybrid model called LR XGBoost. This model changes a linear regression model to match the predictions of XGBoost. The hybrid model keeps the strong predictive power of complex models but makes the results easier to understand, which is important for making decisions in retail. Our study shows that our hybrid model offers a good balance, providing reliable sales forecasts with more transparency than standard linear regression. This makes it a valuable tool for retail managers who need accurate forecasts and a clear understanding of what influences sales. The model’s consistent performance across datasets also suggests it can be used in various retail settings to improve efficiency and help with strategic decisions. © 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)

Abstract
We propose a statistical duality among the preferences and endowments of the agents. Under this duality, the logarithmic prices of random trades among agents in a decentralized economy converge in expectation to the logarithm of the Walrasian equilibrium price in a centralized economy.

Abstract
Among transportation researchers, pedestrian issues are highly significant, and various solutions have been proposed to address these challenges. These approaches include Multi-Criteria Decision Analysis (MCDA) and machine learning (ML) techniques, often categorized into two primary types. While previous studies have addressed diverse methods and transportation issues, this research integrates pedestrian modeling with MCDA and ML approaches. This paper examines how MCDA and ML can be combined to enhance decision-making in pedestrian dynamics. Drawing on a review of 1574 papers published from 1999 to 2023, this study identifies prevalent themes and methodologies in MCDA, ML, and pedestrian modeling. The MCDA methods are categorized into weighting and ranking techniques, with an emphasis on their application to complex transportation challenges involving both qualitative and quantitative criteria. The findings suggest that hybrid MCDA algorithms can effectively evaluate ML performance, addressing the limitations of traditional methods. By synthesizing the insights from the existing literature, this review outlines key methodologies and provides a roadmap for future research in integrating MCDA and ML in pedestrian dynamics. This research aims to deepen the understanding of how informed decision-making can enhance urban environments and improve pedestrian safety.

Abstract
This paper fits in the theory of international agreements by studying the success of stable coalitions of agents seeking the preservation of a public good. Extending Baliga and Maskin, we consider a model of N homogeneous agents with quasi-linear utilities of the form u(j) (r(j); r) = r(alpha) - r(j), where r is the aggregate contribution and the exponent alpha is the elasticity of the gross utility. When the value of the elasticity alpha increases in its natural range (0, 1), we prove the following five main results in the formation of stable coalitions: (i) the gap of cooperation, characterized as the ratio of the welfare of the grand coalition to the welfare of the competitive singleton coalition grows to infinity, which we interpret as a measure of the urge or need to save the public good; (ii) the size of stable coalitions increases from 1 up to N; (iii) the ratio of the welfare of stable coalitions to the welfare of the competitive singleton coalition grows to infinity; (iv) the ratio of the welfare of stable coalitions to the welfare of the grand coalition decreases (a lot), up to when the number of members of the stable coalition is approximately N/e and after that it increases (a lot); and (v) the growth of stable coalitions occurs with a much greater loss of the coalition members when compared with free-riders. Result (v) has two major drawbacks: (a) A priori, it is difficult to convince agents to be members of the stable coalition and (b) together with results (i) and (iv), it explains and leads to the pessimistic Barrett's paradox of cooperation, even in a case not much considered in the literature: The ratio of the welfare of the stable coalitions against the welfare of the grand coalition is small, even in the extreme case where there are few (or a single) free-riders and the gap of cooperation is large. Optimistically, result (iii) shows that stable coalitions do much better than the competitive singleton coalition. Furthermore, result (ii) proves that the paradox of cooperation is resolved for larger values of.. so that the grand coalition is stabilized.

Abstract

Abstract
Data sets that contain an excessive number of zeros appear in several fields of applications. This chapter considers a zero-inflated Lomax distribution as a possible model for these types of data, and presents and analyzes the performance of a Shewhart control chart for process monitoring. Several approaches allow for frequent zero observations, and among them, the most common are zero-inflated models and hurdle models in case of count data, and the use of zero-inflated distributions to model semi-continuous data, that is, data from a continuous distribution with one or more than one point of mass. The chapter presents some motivation for the use of the zero-inflated Lomax distribution together with some properties of this distribution. It proposes a Shewhart-type control chart for monitoring zero-inflated Lomax data, and analyzes its performance under some scenarios.