Search Results (26)

The Maxwell–Boltzmann (MB) distribution is fundamental in statistical physics, providing an exact description of particle speed or energy distributions. In this study, a discrete formulation derived via the survival function discretization technique extends the MB model’s theoretical strengths to realistically handle lifetime and reliability data recorded in integer form, enabling accurate modeling under inherently discrete or censored observation schemes. The proposed discrete MB (DMB) model preserves the continuous MB’s flexibility in capturing diverse hazard rate shapes, while directly addressing the discrete and often censored nature of real-world lifetime and reliability data. Its formulation accommodates right-skewed, left-skewed, and symmetric probability mass functions with an inherently increasing hazard rate, enabling robust modeling of negatively skewed and monotonic-failure processes where competing discrete models underperform. We establish a comprehensive suite of distributional properties, including closed-form expressions for the probability mass, cumulative distribution, hazard functions, quantiles, raw moments, dispersion indices, and order statistics. For parameter estimation under Type-II censoring, we develop maximum likelihood, Bayesian, and bootstrap-based approaches and propose six distinct interval estimation methods encompassing frequentist, resampling, and Bayesian paradigms. Extensive Monte Carlo simulations systematically compare estimator performance across varying sample sizes, censoring levels, and prior structures, revealing the superiority of Bayesian–MCMC estimators with highest posterior density intervals in small- to moderate-sample regimes. Two genuine datasets—spanning engineering reliability and clinical survival contexts—demonstrate the DMB model’s superior goodness-of-fit and predictive accuracy over eleven competing discrete lifetime models. Full article

Energy security has emerged as a critical concern amid intensifying climate risks and surging energy demand driven by economic growth. This study examines the impact of climate risk on energy security by constructing a panel dataset covering 30 Chinese provinces from 2006 to 2022. Using the instrumental variable generalized method of moments (IV-GMM) model, we estimate the marginal impact of climate risk on energy security and further investigate its asymmetric, direct, and indirect relationships via panel quantile regression and mediation analysis. Our key findings are as follows: (1) Climate risk exerts a significant negative impact on energy security, indicating an inverse relationship. (2) The effect of climate risk is asymmetric, with a stronger adverse impact in regions with lower levels of energy security. (3) Climate risk undermines energy security by reducing energy accessibility, affordability, sustainability, and technological efficiency. (4) Energy transition and energy efficiency serve as critical mediators in the relationship between climate risk and energy security, offering insights into potential mitigation pathways. Unlike previous studies that primarily examine energy security in isolation or focus on single dimensions, this research integrates a multidimensional indicator system and advanced econometric techniques to uncover both direct and mediated pathways, thereby filling a key gap in understanding the climate–energy nexus at the provincial level in China. Based on these findings, we propose targeted policy recommendations to enhance energy security by improving climate resilience, accelerating the deployment of renewable energy, and optimizing energy infrastructure investments. Full article

This study introduces an inverted version of the three-parameter Hjorth lifespan model, characterized by one scale parameter and two shape parameters, referred to as the inverted Hjorth (IH) distribution. This asymmetric distribution can fit various positively skewed datasets more accurately than several existing models in the literature, as it can accommodate data exhibiting an inverted (upside-down) bathtub-shaped hazard rate. We derive key properties of the model, including quantiles, moments, reliability measures, stress–strength reliability, and order statistics. Point estimation of the IH model parameters is performed using maximum likelihood and Bayesian approaches. Moreover, for interval estimation, two types of asymptotic confidence intervals and two types of Bayesian credible intervals are obtained using the same estimation methodologies. As an extension to a complete sampling plan, Type-II censoring is employed to examine the impact of data incompleteness on IH parameter estimation. Monte Carlo simulation results indicate that Bayesian point and credible estimates outperform those obtained via classical estimation methods across several precision metrics, including mean squared error, average absolute bias, average interval length, and coverage probability. To further assess its performance, two real datasets are analyzed: one from the environmental domain (minimum monthly water flows of the Piracicaba River) and another from the pharmacological domain (plasma indomethacin concentrations). The superiority and flexibility of the inverted Hjorth model are evaluated and compared with several competing models. The results confirm that the IH distribution provides a better fit than several existing lifetime models—such as the inverted Gompertz, inverted log-logistic, inverted Lomax, and inverted Nadarajah–Haghighi distributions—making it a valuable tool for reliability and survival data analysis. Full article

This paper introduces a novel and flexible class of continuous probability distributions, termed the Alpha Power Survival Ratio-X (APSR-X) family. Unlike many existing transformation-based families, the APSR-X class integrates an alpha power transformation with a survival ratio structure, offering a new mechanism for enhancing shape flexibility while maintaining mathematical tractability. This construction enables fine control over both the tail behavior and the symmetry properties, distinguishing it from traditional alpha power or survival-based extensions. We focus on a key member of this family, the two-parameter Alpha Power Survival Ratio Exponential (APSR-Exp) distribution, deriving essential mathematical properties including moments, quantile functions and hazard rate structures. We estimate the model parameters using eight frequentist methods: the maximum likelihood (MLE), maximum product of spacings (MPSE), least squares (LSE), weighted least squares (WLSE), Anderson–Darling (ADE), right-tailed Anderson–Darling (RADE), Cramér–von Mises (CVME) and percentile (PCE) estimation. Through comprehensive Monte Carlo simulations, we evaluate the estimator performance using bias, mean squared error and mean relative error metrics. The proposed APSR-X framework uniquely enables preservation or controlled modification of the symmetry in probability density and hazard rate functions via its shape parameter. This capability is particularly valuable in reliability and survival analyses, where symmetric patterns represent balanced risk profiles while asymmetric shapes capture skewed failure behaviors. We demonstrate the practical utility of the APSR-Exp model through three real-world applications: economic (tax revenue durations), engineering (mechanical repair times) and medical (infection durations) datasets. In all cases, the proposed model achieves a superior fit over that of the conventional alternatives, supported by goodness-of-fit statistics and visual diagnostics. These findings establish the APSR-X family as a unique, symmetry-aware modeling framework for complex lifetime data. Full article

Amid escalating environmental crises—ranging from biodiversity loss to climate instability—the circular economy has emerged as a promising pathway to align economic growth with ecological limits. The objective of this study is to examine the asymmetric impact of a novel composite circular economy index (CEI)—constructed via entropy weighting—on the load capacity factor (LCF), a holistic sustainability metric, across 27 EU member states over 2010–2023. Employing the method of moments quantile regression (MMQR) and controlling for GDP, foreign direct investment, trade openness, employment, and population growth, the main findings indicate pronounced heterogeneity: positive CEI shocks yield a 1.219 percent increase in LCF at the 90th quantile versus just 0.229 percent at the 10th, revealing a “sustainability premium” for high-performing economies, while negative shocks inflict a −5.253 percent decline at the 90th quantile, exposing their greater vulnerability. Low-LCF countries, by contrast, display relative resilience to downturns, likely due to less entrenched circular systems. Panel Granger causality tests further reveal bidirectional feedback loops between LCF and economic growth, investment, and labor markets, alongside a unidirectional effect from trade openness to enhanced sustainability. These insights carry clear policy implications: high-LCF nations require safeguards against circularity backsliding, whereas low-LCF members need capacity-building to convert latent resilience into sustained gains—together forming a nuanced blueprint for achieving the EU’s 2050 climate-neutrality ambitions. Full article

This study introduces the sine unit exponentiated half-logistic distribution, a novel extension of the unit exponentiated half-logistic distribution within the sine-G family. Using trigonometric transformations, the proposed distribution offers flexible density shapes for modeling asymmetric unit-interval data. We derive its statistical properties, including quantiles, moments, and stress–strength reliability, and estimate parameters via classical methods like maximum likelihood and Anderson–Darling. Simulations and real-world applications to fiber strength and burr datasets demonstrate the superior fit of the proposed distribution over competing models, highlighting its utility in reliability engineering and manufacturing. Full article

This research explores the relationship between credit risk and bank value within the framework of horizontal mergers and acquisitions (M&A), employing a quantile regression approach to analyze how horizontal M&A activities moderate this relationship across 110 operational Bank Holding Companies (BHCs) over 23 years. This paper stands out from previous studies by extending the scope beyond linear approaches and using the Quantiles via Moments estimator to address potential endogeneity concerns. The results demonstrate a significant negative link between credit risk and bank value, which decreases in magnitude as moving higher in the value distribution. Conversely, there is a consistent positive connection between M&A activities and bank value that is stable across different quantiles of value. Mergers and acquisitions worsen the negative impact of credit risk on bank value, affecting banks with both low and high values similarly. The findings provide useful information for investors, practitioners, and policymakers in the banking industry. Investors may use credit risk and value proposition assessments to make well-informed investment decisions, or to construct well-diversified portfolios, and identify appropriate institutions for mergers and acquisitions to enhance value. It is recommended that practitioners prioritize efficient credit risk management, especially before engaging in M&A activities and aligning them with the bank’s value proposition. Policymakers should develop guidelines to regulate M&A transactions, using established dynamic credit risk standards that correspond to banks’ value propositions, to promote financial stability and drive industry expansion. Full article

Accurate quantile estimation of extreme precipitation is crucial for hydraulic infrastructure design but is often hindered by limited data records, leading to uncertainties. This study applies regional frequency analysis (RFA) using L-moments, comparing classical and Bayesian approaches to quantify uncertainties. Data from 55 rainfall stations in Thessaly, Greece, are analyzed through clustering using PCA and k-means. The Generalized Extreme Value (GEV) distribution is fitted to delineated clusters, and uncertainties are assessed via bootstrap and MCMC methods. Results highlight consistency in location and scale estimates, with Bayesian methods offering narrower uncertainty bounds, demonstrating improved reliability for long-term rainfall prediction and design. Full article

Limitations inherent to existing statistical distributions in capturing the complexities of real-world data often necessitate the development of novel models. This paper introduces the new exponential generalized inverse generalized Weibull (NEGIGW) distribution. The NEGIGW distribution boasts significant flexibility with symmetrical and asymmetrical shapes, allowing its hazard rate function to be adapted to many failure patterns observed in various fields such as medicine, biology, and engineering. Some statistical properties of the NEGIGW distribution, such as moments, quantile function, and Renyi entropy, are studied. Three methods are used for parameter estimation, including maximum likelihood, maximum product of spacing, and percentile methods. The performance of the estimation methods is evaluated via Monte Carlo simulations. The NEGIGW distribution excels in its ability to fit real-world data accurately. Five medical and engineering datasets are applied to demonstrate the superior fit of NEGIGW distribution compared to competing models. This compelling evidence suggests that the NEGIGW distribution is promising for lifetime data analysis and reliability assessments across different disciplines. Full article

This study proposes a new five-parameter distribution called the gamma-exponentiated Weibull–Poisson (GEWP) distribution. As an extension of the exponentiated Weibull–Poisson family, the GEWP distribution offers a more flexible tool for analyzing a wider variety of data due to its theoretically and practically advantageous properties. It encompasses established distributions like the exponential, Weibull, and exponentiated Weibull. The development of the GEWP distribution proposed in this paper is obtained by combining the gamma–exponentiated Weibull (GEW) and the exponentiated Weibull–Poisson (EWP) distributions. Therefore, it serves as an extension of both the GEW and EWP distributions. This makes the GEWP a viable alternative for describing the variability of occurrences, enabling analysis in situations where GEW and EWP may be limited. This paper analyzes the probability distribution functions and provides the survival and hazard rate functions, the sub-models, the moments, the quantiles, and the maximum likelihood estimation of the GEWP distribution. Then, the numerical experiments for the parameter estimation of GEWP distribution for some finite sample sizes are presented. Finally, the comparative study of GEWP distribution and its sub-models is investigated via the goodness of fit test with real datasets to illustrate its potentiality. Full article

The effect of trade-related government expenditure on backward and forward participation in global value chains (GVCs) is at the heart of the present analysis. The latter builds on an unbalanced panel dataset of 74 developing countries over the annual period from 2005 to 2018. It has used several estimators, the primary one being the Quantile via Moments approach. The outcomes suggest that trade-related government expenditure exerts no significant effect on countries’ forward participation in GVCs. At the same time, countries located in the 20th to 90th quantiles experience a positive and significant effect of trade-related government expenditure on backward participation in GVCs, with the magnitude of this positive effect being larger for countries in the upper quantiles than for countries in the lower quantiles. The least integrated countries into the backward participation in GVCs (i.e., those in the 10th quantile) experience no significant effect of trade-related government expenditure on backward participation in GVCs. Interestingly, expenditure in favour of developing economic infrastructure, and expenditure for enhancing productive capacities reinforce each other in positively affecting backward GVC participation by countries located in the upper quantiles (i.e., the 50th to 90th quantiles). However, the interaction between these two types of trade-related government expenditure does not influence countries’ forward participation in GVCs. These findings shed light on the importance of trade-related expenditure for enhancing developing countries’ participation in backward GVCs. Full article

Deglobalization, as opposed to the term globalization, appears in the world order due to local solutions to problems and border controls, ignoring the principles of treaties, trade wars, and the expansion of regionalism. In addition, slowbalization helps shrink the global flow of trade, information, and societal and cultural exchange dynamism. However, this scary global order, as triggered by deglobalization and slowbalization, significantly impacts the income factors of allied nations. Against this background, we aim to investigate whether deglobalization and slowbalization proxied by the influencing magnitudes of globalization dimensions (e.g., globalization de facto and de jure, internet diffusions, and trade openness) impact the income inequality of the 12 post-Soviet countries, considering the panel data during 1991–2019. To this end, we apply the quantiles via moments approach to investigate the time-varying connectedness between variables that have country and data-centric heterogeneities. Our findings depict that deglobalization is futile in affecting the post-Soviet countries’ income dynamics, as globalization negatively affects income inequality in diverse quantiles. Specifically, globalization de facto (globalized policy-implementation spectrum) and internet diffusions have a significantly negative influence on reducing income inequality from low to medium quantiles (q.25–q.75). Globalization de jure (globalized policy-decision spectrum) and trade openness are statistically insignificant in entire quantiles (q.25–q.95), implying the likely existence of slowbalization. Finally, government expenditures and governance quality are monotonically negative in reducing income inequality at all quantiles (q.25–q.95). Therefore, policy suggestions enclose galvanizing globalization potentials in curbing income inequality to keep away the distressful phases of deglobalization and slowbalization. Full article

The unit–power Burr X distribution (UPBXD), a bounded version of the power Burr X distribution, is presented. The UPBXD is produced through the inverse exponential transformation of the power Burr X distribution, which is also beneficial for modelling data on the unit interval. Comprehensive analysis of its key characteristics is performed, including shape analysis of the primary functions, analytical expression for moments, quantile function, incomplete moments, stochastic ordering, and stress–strength reliability. Rényi, Havrda and Charvat, and d-generalized entropies, which are measures of uncertainty, are also obtained. The model’s parameters are estimated using a Bayesian estimation approach via symmetric and asymmetric loss functions. The Bayesian credible intervals are constructed based on the marginal posterior distribution. Monte Carlo simulation research is intended to test the accuracy of various estimators based on certain measures, in accordance with the complex forms of Bayesian estimators. Finally, we show that the new distribution is more appropriate than certain other competing models, according to their application for COVID-19 in Saudi Arabia and the United Kingdom. Full article

Government intervention is imperative in the mixed economic system due to market failures, imperfection, pure public goods, and economic externalities. To this end, we measure the comparative impact of budget deficits on economic growth, incorporating the moderating role of quality of governance (QOG) for welfare and non-welfare countries. We apply a newly developed econometric model, namely Panel Quantile Regression via Moment Conditions, considering the scale and location effect due to high heterogeneity in our panel time series data over 1990–2020. Our empirical investigation shows that the budget deficit promotes economic growth sustainability in the overall sample countries. The comparative analysis confirms that budget deficit promotes economic growth for welfare countries while it impends for non-welfare countries. Furthermore, QOG augments sustainable economic growth in different economic circumstances in welfare countries and non-welfare countries. Finally, the results also demonstrate that the QOG plays a supportive role in the nexus between budget deficit and economic growth in the full sample countries. The findings indicate that the effectiveness of the budget deficit varies across welfare and non-welfare countries. In general, QOG promotes economic growth, but its stringent rules and restrictions somewhat slow down the wheel of the growth process. We provide several policy implications. Full article

In this article, we present a new statistical modification of the Weibull model for updating the flexibility, called the generalized Weibull-Weibull distribution. The new modification of the Weibull model is defined and studied in detail. Some mathematical and statistical functions are studied, such as the quantile function, moments, the information generating measure, the Shannon entropy and the information energy. The joint distribution functions of the two marginal univariate models via the Copula model are provided. The unknown parameters are estimated using the maximum likelihood method and Bayesian method via Monte Carlo simulations. The Bayesian approach is discussed using three different loss functions: the quadratic error loss function, the LINEX loss function, and the general entropy loss function. We perform some numerical simulations to show how interesting the theoretical results are. Finally, the practical application of the proposed model is illustrated by analyzing two applications in the actuarial and engineering fields using corporate data to show the elasticity and advantage of the proposed generalized Weibull-Weibull model. The practical applications show that proposed model is very suitable for modeling actuarial and technical data sets and other related fields. Full article