Search Results (35)

This paper addresses the problem of formulating generalized, non-extensive information-theoretic measures on finite non-distributive algebraic structures equipped with Riečan states, with particular emphasis on product Sheffer stroke basic algebras. Our approach formalizes finite summations, admissible partitions, refinement relations, and Sheffer stroke joint refinement candidates by using the primitive Sheffer stroke operation, with partition and marginalization properties imposed under the stated product and admissibility assumptions. By leveraging the state-theoretic properties of Riečan states, we construct baseline Shannon and logical entropies alongside algorithmic procedures for their computational evaluation. As the main result, we introduce and analytically characterize a parametric Tsallis entropy functional over these basic algebras. We prove its fundamental properties, including bounding inequalities, state concavity, monotonicity under refinement, subadditivity (for $\alpha >1$), conditional chain-type identities under the relevant joint refinement marginalization assumptions, and exact analytical convergence to the classical Shannon limit as the entropic index $\alpha \to 1$. Furthermore, under a state-dependent statistical independence condition, we show that the joint Tsallis entropy satisfies a pseudo-additive relation. By defining the Tsallis mutual information and the associated pseudo-additive residual, we isolate the deviation of a joint Sheffer stroke refinement from the factorized model determined by its marginal Riečan-state distributions. This residual is intended as a state-dependent algebraic indicator of deviations from the factorized Tsallis pseudo-additive model; it is not claimed to be an operational contextuality witness, a contextuality inequality, an entanglement measure, or a physical implementation criterion. Full article

The quality and safety supervision of agricultural products at the grassroots level has long faced the triple superposition dilemma of small-sample sampling, multi-source evidence conflict, and risk chain evolution. Although existing data-driven models have considerable accuracy, they are difficult to leverage for intervention decisions, and the simple serial connection of traditional Bayesian networks and evidence theory cannot respond to dynamic scenarios. Aiming at this research gap, this paper constructs a dynamic risk assessment model, CIBE-DR, that deeply couples Bayesian networks with evidential reasoning. It contains three core innovations. First, the structure learning method of the causally identifiable Bayesian network embeds a graded do-calculus identifiability score covering both back-door and front-door criteria into the BDeu scoring function and combines this reward with an expert-prior divergence penalty that breaks Markov equivalence so as to realize the transition from relevance modeling to intervention decision modeling. Second, the conflict-aware adaptive evidence synthesis rule orthogonally decomposes multi-source conflict into an epistemic component and an ontological component, which are modeled respectively by Tsallis belief entropy and abductive inference over a discrete twenty-seven-point heterogeneity hypothesis space and are then fused under a reparameterized Dempster–Yager interpolation in which the two endpoints recover the two named rules under a single consistent interpretation. Third, the bidirectional closed-loop coupling mechanism between BN and ER realizes the mutual calibration between the conditional probability table and the evidence credibility prior under a Lyapunov monotone descent argument with the explicit Lipschitz bound $L_{\theta }$ ≤ 0.028 < 1, endowing the model with time-varying self-correction ability. Based on experiments on 156,847 sampling samples from counties and townships in East China, Central China, and Southwest China from 2021 to 2024, the proposed method achieved the best value in six of the seven evaluation indicators, with a minority recall of 0.864 ± 0.014, an intervention effect estimation error of 0.063 ± 0.005, and a dynamic response delay of 2.8 ± 0.3 days, significantly ahead of eleven mainstream baselines under the McNemar test on classification ($p$ < 0.001) and the Wilcoxon signed-rank test on intervention-effect estimation ($p$ < 0.001). The only indicator on which CIBE-DR does not lead is overall accuracy, which is 0.002 lower than that of Transformer; this difference does not reach statistical significance under the McNemar test ($p$ = 0.32) and does not weaken the value of grassroots supervision in the strong-imbalance scenario where the positive rate is only 1.04%. The robustness advantage of the model is particularly prominent in the scenarios of sparse data, adversarial perturbation, and prior-graph incompleteness, and the intervention-effect estimates were additionally validated against two post-2022 policy interventions with absolute deviations of 1.4 and 1.2 percentage points respectively. These results verify the product gain and grassroots deployability of the three mechanisms. Full article

Testing exponentiality against increasing failure rate alternatives is central to reliability theory and lifetime data analysis. This paper develops the Adaptive Cumulative Residual Entropy Test under Proportional Hazards (Adaptive CRE-PH Test), a scale-invariant nonparametric procedure that unifies a Tsallis-entropy departure functional with a proportional-hazards transformation. For each tuning value, the fixed-$q$ statistic admits a normalized-spacing representation. Under exponentiality, the spacing proportions follow a Dirichlet distribution, yielding exact finite-sample means, covariances, and a joint null characterization of the adaptive maximum. Joint asymptotic normality and consistency under fixed alternatives are established for the complete dependent score vector. Structural analysis of the score family motivates a prespecified moderate grid governed by endpoint stability, directional diversity, and multiplicity economy, rather than retrospective power optimization. Monte Carlo experiments demonstrate accurate size control, explicitly quantify calibration stability, and show power close to the best fixed-$q$ component under linear failure rate, Makeham, and Weibull alternatives. A dedicated power experiment confirms substantial detection capability against an IFRA-but-not-IFR benchmark, showing that the broader population sign condition has practical as well as theoretical relevance. Additional DFR and bathtub experiments clarify directional specificity: rejection provides evidence against exponentiality in the IFR-sensitive direction but does not, without shape-specific inference, establish a globally increasing hazard. Three real-data applications illustrate the practical importance of distinguishing formal directional inference from exploratory Q–Q and total-time-on-test diagnostics. Full article

We propose the three-parameter Yun–Linear Exponential (YLE) distribution, with a specific focus on its comprehensive characterizations based on truncated moments, hazard functions, and conditional expectations. In addition, a hazard-based characterization is empirically illustrated through a diagnostic plot that compares the theoretical characterization function with its empirical counterpart, providing further support for the proposed model. To provide a comprehensive analysis of the model’s information content, we evaluate a collection of information measures, including Rényi entropy, Tsallis entropy, extropy, and cumulative residual entropy, alongside fundamental statistical properties, such as ordinary moments, generating function, and quantile function. Model parameters are estimated using the maximum-likelihood method, with their performance and finite-sample properties validated through extensive Monte Carlo simulation studies. Finally, the practical utility of the YLE model is demonstrated through two distinct reliability applications, analyzing MRI scanner failure times and repairable item intervals, confirming its robustness and flexibility in modeling heavily skewed lifetime data. Full article

We study nearest-neighbor-based estimators of Tsallis entropy associated with Poisson and binomial point processes on general metric measure spaces. In this study, by combining existing stabilization methods with the validation of the estimator’s local k-nearest-neighbor structure, we investigate nearest-neighbor-based Tsallis entropy estimators under Poisson and binomial distributed input data. Rather than proposing a new second-order Poincaré inequality, this paper details and clearly presents stabilization-based normal approximation bounds for Tsallis-type k-NN functionals. We establish asymptotic normality and derive explicit convergence rates for the Kolmogorov distance. Our analysis avoids explicit score-function decompositions and instead relies on flexible localizations of add-one costs, which simplify the treatment of higher-order terms. Under natural stabilization and moment conditions, the resulting bounds recover the classical normal approximation rates $s^{-1/2}$ and $n^{-1/2}$ and extend corresponding results for Shannon and Rényi entropy estimators. We further illustrate the scope of the framework through examples involving Tsallis entropy functionals, weighted k-NN Shannon entropy estimators. The examples provided highlight the benefits of stabilization-based normal approximations for non-parametric statistical inference in complex spatial and high-dimensional settings. Full article

The paper explored the fractal, nonlinear and chaotic dynamics between oil prices, inflation, economic growth and unemployment in Turkiye from 1960 to 2024 and examined how energy market volatility propagated through the macroeconomy via complex, regime-dependent mechanisms. It developed a chaotic regression method and employed entropy-based measures (Shannon, Rényi and Tsallis), Lyapunov exponents, Lorenz and Rössler attractors, Julia set diagnostics and the chaos Granger causality test (Hiemstra–Jones). By nesting entropy, chaos and causality within a unified framework, it contributed methodological innovations and practical insights to the energy–economy literature. The chaotic regression results revealed that oil price shocks generated asymmetric and nonlinear responses in inflation, unemployment and growth that were characterized by chaos and sensitivity to initial conditions and demonstrated that oil shocks act as catalysts for nonlinear propagation and fractal macroeconomic dynamics. Julia set results determined that unemployment can be explained by inflation fractal size. Hiemstra–Jones method determined unidirectional causality from oil to both inflation, economic growth and unemployment. According to the results, adopting nonlinear and chaos-based modeling approaches is essential to understand the macroeconomic consequences of energy shocks. For policymakers, the evidence determined that the costs of disinflation or inflation control are sensitive to energy market volatility. The paper contributed to the energy–economy-econometrics literature by integrating entropy, chaos and causality analyses into the oil price–macroeconomy nexus by offering both methodological innovations and practical insights. Full article

We introduce and study the shortfall of tail-based entropy (STE), a tail-sensitive risk functional that combines expected shortfall (ES) and tail-based entropy (TE). Beyond the tail mean, STE imposes a rank-dependent penalty on tail variability, thereby capturing both the magnitude and variability of tail risk under extremes. The framework encompasses several shortfall-type measures as special cases, such as Gini shortfall, extended Gini shortfall, shortfall of cumulative residual entropy, shortfall of right-tail deviation, and shortfall of cumulative residual Tsallis entropy. We provide equivalent characterizations of STE, derive sufficient conditions for coherence, and establish monotonicity with respect to tail-variability order. As an application, we investigate STE-based capital allocation, deriving closed-form allocation formulas under elliptical and extended skew-normal distributions, along with several illustrative special cases. Finally, an empirical analysis with insurance company data illustrates the implementation and evaluates the performance of the allocation rule. Full article

Portfolio optimization is a cornerstone of modern financial decision-making, traditionally based on the mean–variance model introduced by Markowitz. However, this framework relies on restrictive assumptions—such as normally distributed returns and symmetric risk preferences—that often fail in real-world markets, particularly in volatile and non-Gaussian environments such as cryptocurrencies. To address these limitations, this paper proposes a novel multi-objective model that combines expected return maximization, mean absolute deviation (MAD) minimization, and entropy-based diversification into a unified optimization structure: the Mean–Deviation–Entropy (MDE) model. The MAD metric offers a robust alternative to variance by capturing the average magnitude of deviations from the mean without inflating extreme values, while entropy serves as an information-theoretic proxy for portfolio diversification and uncertainty. Three entropy formulations are considered—Shannon entropy, Tsallis entropy, and cumulative residual Sharma–Taneja–Mittal entropy (CR-STME)—to explore different notions of uncertainty and structural diversity. The MDE model is formulated as a tri-objective optimization problem and solved via scalarization techniques, enabling flexible trade-offs between return, deviation, and entropy. The framework is empirically tested on a cryptocurrency portfolio composed of Bitcoin (BTC), Ethereum (ETH), Solana (SOL), and Binance Coin (BNB), using daily data over a 12-month period. The empirical setting reflects a high-volatility, high-skewness regime, ideal for testing entropy-driven diversification. Comparative outcomes reveal that entropy-integrated models yield more robust weightings, particularly when tail risk and regime shifts are present. Comparative results against classical mean–variance and mean–MAD models indicate that the MDE model achieves improved diversification, enhanced allocation stability, and greater resilience to volatility clustering and tail risk. This study contributes to the literature on robust portfolio optimization by integrating entropy as a formal objective within a scalarized multi-criteria framework. The proposed approach offers promising applications in sustainable investing, algorithmic asset allocation, and decentralized finance, especially under high-uncertainty market conditions. Full article

Standard correlation analysis is one of the frequently used methods in financial markets. However, this matrix can give erroneous results in the conditions of chaos, fractional systems, entropy, and complexity for the variables. In this study, we employed the time-dependent correlation matrix based on isospectral flow using the Lie group method to assess the price of Bitcoin and gold from 19 July 2010 to 31 December 2024. Firstly, we showed that the variables have a chaotic and fractional structure. Lo’s rescaled range (R/S) and the Mandelbrot–Wallis method were used to determine fractionality and long-term dependence. We estimated and tested the d parameter using GPH and Phillips’ estimators. Renyi, Shannon, Tsallis, and HCT tests determined entropy. The KSC determined the evidence of the complexity of the variables. Hurst exponents determined mean reversion, chaos, and Brownian motion. Largest Lyapunov and Hurst exponents and entropy methods and KSC found evidence of chaos, mean reversion, Brownian motion, entropy, and complexity. The BDS test determined nonlinearity, and later, the time-dependent correlation matrix was obtained by using the stochastic SO(2) Lie group. Finally, we obtained robustness check results. Our results showed that the time-dependent correlation matrix obtained by using the stochastic SO(2) Lie group method yielded more successful results than the ordinary correlation and covariance matrix and the Spearman correlation and covariance matrix. If policymakers, financial managers, risk managers, etc., use the standard correlation method for economy or financial policies, risk management, and financial decisions, the effects of nonlinearity, fractionality, entropy, and chaotic structures may not be fully evaluated or measured. In such cases, this can lead to erroneous investment decisions, bad portfolio decisions, and wrong policy recommendations. Full article

This study investigates systemic risk, return patterns, and diversification within the Johannesburg Stock Exchange (JSE) during the COVID-19 pandemic, utilizing data-centric approaches and the ARMA-GARCH vine copula-based conditional value-at-risk (CoVaR) model. By comparing three investment strategies—industry sector-based, asset risk–return plot-based, and clustering-based—this research reveals that the industrial and technology sectors show no ARCH effects and remain isolated from other sectors, indicating potential diversification opportunities. Furthermore, the analysis employs C-vine and R-vine copulas, which uncover weak tail dependence among JSE sectors. This finding suggests that significant fluctuations in one sector minimally impact others, thereby highlighting the resilience of the South African economy. Additionally, entropy measures, including Shannon and Tsallis entropy, provide insights into the dynamics and predictability of various portfolios, with results indicating higher volatility in the energy sector and certain clusters. These findings offer valuable guidance for investors and policymakers, emphasizing the need for adaptable risk management strategies, particularly during turbulent periods. Notably, the industrial sector’s low CoVaR values signal stability, encouraging risk-tolerant investors to consider increasing their exposure. In contrast, others may explore diversification and hedging strategies to mitigate risk. Interestingly, the industry sector-based portfolio demonstrates better diversification during the COVID-19 crisis than the other two data-centric portfolios. This portfolio exhibits the highest Tsallis entropy, suggesting it offers the best diversity among the types analyzed, albeit said diversity is still relatively low overall. However, the portfolios based on groups and clusters of sectors show similar levels of diversity and concentration, as indicated by their identical entropy values. Full article

Has the mean-variance framework become obsolete? In this paper, we replace traditional variance–covariance methods of portfolio optimisation with relative Tsallis entropy and mutual information measures. Its goal is to enhance risk management and diversification in complicated finance ecosystems. We utilize the S&P 500 and Bitwise 10 cryptocurrency indices’ daily returns (2019–2024 data) and conduct our analysis to the year 2020 under extreme shocks. Many models were trained with different configurations, like mean-variance (MV), mean-entropy (ME), and mean-mutual information (MI) traders and their corresponding variants, using Sharpe’s ratio, Jensen’s alpha, and entropy value of risk (EVAR). The findings indicate that entropic models outperform conventional models in terms of diversification and, especially, extreme risk management. Because the appropriate normalization conditions often fail to be satisfied, we can informally see that after a recalibration of the effective frontier, we obtain from EVAR an accumulated resilience aspect to these rare events while also observing the great potential of entropy-based models to replicate non-linear dependencies between assets. The results show that models combining entropy and mutual information optimise the gain–loss ratio (GLR), providing stable diversification and improved risk management, while maximising returns in complex and volatile market environments. Full article

Metaverse (MV) technology introduces new tools for users each day. MV companies have a significant share in the total stock markets today, and their size is increasing. However, MV technologies are questioned as to whether they contribute to environmental pollution with their increasing energy consumption (EC). This study explores complex nonlinear contagion with tail dependence and causality between MV stocks, EC, and environmental pollution proxied with carbon dioxide emissions (CO₂) with a decade-long daily dataset covering 18 May 2012–16 March 2023. The Mandelbrot–Wallis and Lo’s rescaled range (R/S) tests confirm long-term dependence and fractionality, and the largest Lyapunov exponents, Shannon and Havrda, Charvât, and Tsallis (HCT) entropy tests followed by the Kolmogorov–Sinai (KS) complexity measure confirm chaos, entropy, and complexity. The Brock, Dechert, and Scheinkman (BDS) test of independence test confirms nonlinearity, and White‘s test of heteroskedasticity of nonlinear forms and Engle’s autoregressive conditional heteroskedasticity test confirm heteroskedasticity, in addition to fractionality and chaos. In modeling, the marginal distributions are modeled with Markov-Switching Generalized Autoregressive Conditional Heteroskedasticity Copula (MS-GARCH–Copula) processes with two regimes for low and high volatility and asymmetric tail dependence between MV, EC, and CO₂ in all regimes. The findings indicate relatively higher contagion with larger copula parameters in high-volatility regimes. Nonlinear causality is modeled under regime-switching heteroskedasticity, and the results indicate unidirectional causality from MV to EC, from MV to CO_2, and from EC to CO₂, in addition to bidirectional causality among MV and EC, which amplifies the effects on air pollution. The findings of this paper offer vital insights into the MV, EC, and CO₂ nexus under chaos, fractionality, and nonlinearity. Important policy recommendations are generated. Full article

With the help of Tsallis residual entropy, we introduce Tsallis quantile entropy order between two random variables. We give necessary and sufficient conditions, study closure and reversed closure properties under parallel and series operations and show that this order is preserved in the proportional hazard rate model, proportional reversed hazard rate model, proportional odds model and record values model. Full article

This work focuses on exploring the properties of past Tsallis entropy as it applies to order statistics. The relationship between the past Tsallis entropy of an ordered variable in the context of any continuous probability law and the past Tsallis entropy of the ordered variable resulting from a uniform continuous probability law is worked out. For order statistics, this method offers important insights into the characteristics and behavior of the dynamic Tsallis entropy, which is associated with past events. In addition, we investigate how to find a bound for the new dynamic information measure related to the lifetime unit under various conditions and whether it is monotonic with respect to the time when the device is idle. By exploring these properties and also investigating the monotonic behavior of the new dynamic information measure, we contribute to a broader understanding of order statistics and related entropy quantities. Full article

During the service process of high-rise buildings, hollowing defects may be produced in the decorative layer, which not only affect the appearance, but also create a safety hazard of wall covering and shattered plaster peeling. Numerous studies have shown that hollowing can be detected using infrared thermal imagery under normal conditions. However, it is difficult to detect the edge and calculate the area of the hollowing on an exterior facade accurately because of the low contrast and fuzzy boundaries of the obtained infrared thermal images. To address these problems, a method for extracting the contours of building facade hollowing defects using polarization thermal images based on an improved Canny algorithm has been proposed in this paper. Firstly, the principle of thermal polarization imaging was introduced for hollowing detection. Secondly, considering the shortcomings of the Canny edge detection algorithm and the features of polarization thermal images, an improved Canny edge detection algorithm is proposed, including adaptive bilateral filtering to improve noise reduction ability while ensuring defect edges are not virtualized, Laplacian sharpening and histogram equalization to achieve contour sharpening and contrast enhancement, and eight-direction gradient templates for calculating image gradients, which make interpolation with non-maximum suppression more accurate, and the Tsallis entropy threshold segmentation algorithm based on the OTSU algorithm verification makes the image contour information more complete and accurate. Finally, a long-wave infrared polarization thermal imaging experimental platform was established and validation experiments were conducted. The experimental results demonstrate that the distinct, smooth, and precise location edges of the hollowing polarization infrared thermal images can be obtained, and the average error of the detected hollowing area is about 10% using the algorithm proposed in this paper. Full article