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In the field of engineering, the fractional moments of random variables play a crucial role and are widely utilized. They are applied in various areas such as structural reliability assessment and analysis, studying the response characteristics of random vibration systems and optimizing signal processing and control systems. This study focuses on calculating the fractional moments of positive random variables encountered in engineering. This study focuses on calculating the fractional moments of positive random variables encountered in engineering.

By integrating Laplace transforms with fractional derivatives, both analytical and practical numerical solutions are derived. Furthermore, specific practical application methods are provided.

This approach allows for the stable and highly accurate calculation of fractional moments based on the integer moments of random variables. Data experiments included in this study demonstrate the effectiveness of this method in solving fractional moment calculations in engineering. Compared to traditional methods, the proposed method offers significant advantages in stability and accuracy, which can further advance research in the engineering field that employs fractional moments.

(1) Accuracy: Although the proposed method does involve some error, its error level is significantly lower than traditional methods, such as the Taylor expansion method. (2) Stability: The computational error of the proposed method is not only minimal but also remains stable within a narrow range as the fractional order varies. (3) Efficiency: Compared to the widely used Taylor expansion method, the proposed method requires only a minimal number of integer-order moments to achieve the desired results. Additionally, it avoids convergence issues during computation, greatly reducing computational resource requirements. (4) Simplicity: The application steps of the proposed method are very straightforward, offering significant advantages in practical applications.

The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits.

First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used.

In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic.

This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases.

The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

In this paper, a mixture of exponential and Rayleigh distributions in the proportions α and 1 − α and all the parameters in the mixture distribution are estimated based on fuzzy data.

The methods such as maximum likelihood estimation (MLE) and method of moments (MOM) are applied for estimation. Fuzzy data of triangular fuzzy numbers and Gaussian fuzzy numbers for different sample sizes are considered to illustrate the resulting estimation and to compare these methods. In addition to this, the obtained results are compared with existing results for crisp data in the literature.

The application of fuzziness in the data will be very useful to obtain precise results in the presence of vagueness in data. Mean square errors (MSEs) of the resulting estimators are computed using crisp data and fuzzy data. On comparison, in terms of MSEs, it is observed that maximum likelihood estimators perform better than moment estimators.

Classical methods of obtaining estimators of unknown parameters fail to give realistic estimators since these methods assume the data collected to be crisp or exact. Normally, such case of precise data is not always feasible and realistic in practice. Most of them will be incomplete and sometimes expressed in linguistic variables. Such data can be handled by generalizing the classical inference methods using fuzzy set theory.

While science has researched the impact of air pollution on human health, the economic dimension of it has been less researched so far. Renewable energy consumption is an important factor in determining the level of life expectancy and reducing health expenditure. Thus, this study aims to investigate the impact of renewable energy, carbon emissions, health expenditure and urbanization on life expectancy in G-7 countries over the period of 2000–2019.

This study has adopted a novel Method of Moments Quantile Regression (MMQR). Furthermore, as a robustness check for MMQR, the fully modified ordinary least square, dynamic ordinary least squares and fixed effect ordinary least square estimators have been used.

The results indicated that renewable energy consumption, health expenditure and urbanization lead to an increase in life expectancy across all quantiles (5th to 95th), whereas higher carbon dioxide emissions reduce life expectancy at birth across all the quantiles (5th to 95th).

The empirical findings conclude that governments should recognize their potential in renewable energy sources and devise policies such as tax-related regulations, or relevant incentives to encourage further investments in this field.

This paper in comparison to the other research studies used MMQR to investigate the impact of factors affecting life expectancy. Also, to the best of the authors’ knowledge, so far no study has investigated the impact of renewable energy on life expectancy in G-7 countries.

In the backdrop of persistent internal and external imbalances, the nexus between fiscal imbalance and current account imbalance remains a subject of debate among economists, policymakers, research scholars and governmental organisations. Nevertheless, there is no definitive consensus, either theoretical or empirical, especially within the SAARC region. This evident lack of unequivocal solid agreement underscores the pressing necessity for further empirical inquiry into the twin deficits hypothesis. In this regard, the present study makes a novel attempt to re-examine the twin deficits hypothesis for major SAARC economies in a non-linear fashion using a balanced data set from 1985 to 2021.

In our empirical analysis, we addressed several methodological challenges in examining the relationship between fiscal balance and current account balance. Initially, we tackled cross-section dependency, heterogeneous slope coefficients and non-stationarity issues. We employed the panel Fourier unit root test by Nazlioglu and Karul to detect smooth breaks and non-linearity. Long-run cointegration was assessed using novel third-generation cointegration tests introduced by Westerlund and Edgerton (2008) and Banerjee and Carrion-i-Silvestre (2017). The non-linear dynamics were examined using the method of moments quantile regression (MMQR). Finally, to investigate the causal relationship between fiscal deficit and current account deficit within a panel framework, we employed the novel JKS test.

The MMQR analysis reveals that the fiscal balance has a positive and significant impact on the current account balance across all quantiles except the lower quantiles (first to third). The magnitude of the coefficient for fiscal balance increases from lower to higher quantiles, suggesting that countries with lower fiscal deficits manage their current account balances more efficiently. Likewise, a positive and significant impact of the saving-investment balance on the current account balance is observed across all quantiles, with the coefficient decreasing as quantiles increase. This indicates that a wider saving-investment gap leads to a more pronounced deterioration in the current account balance. The exchange rate also significantly influences the relationship, highlighting a strong exchange rate channel in transmitting fiscal policy shocks to the current account balance. These findings are corroborated by robustness checks using fully modified ordinary least squares (FMOLS) and dynamic ordinary least squares (DOLS) estimators. The JKS causality test confirms the bi-directional causality between fiscal and current account balances, further validating the results.

Our study has profound policy implications, suggesting that the “size” of fiscal deficit significantly impacts external balances and broader macroeconomic goals in SAARC economies. Policymakers are urged to implement prudent fiscal policies, enhance revenue generation, and promote fiscal discipline to achieve economic stability and sustainability. Minimising unproductive consumer spending and improving tax collections are also recommended to manage external imbalances effectively. Our research offers valuable insights for policymakers and researchers striving to foster sustainable economic development in the SAARC region.

Most macroeconomic variables do not always behave symmetrically and linearly. As a result, it is likely that these variables exhibit asymmetric and non-linear behaviour in response to cyclical and structural changes. Therefore, employing asymmetric and non-linear econometric approaches, rather than the usual symmetrical analysis, to understand the behaviour of the current account and fiscal balance in SAARC economies is rational. Existing empirical studies predominantly focus on the twin deficits hypothesis, neglecting the influence of the saving-investment balance on both fiscal and current account balances. Our research aims to fill this gap by integrating the saving-investment balance into the twin deficits model, thus providing a pioneering analysis that expands our understanding of the relationship between internal and external imbalances. The methodological novelty of our study lies in the fact that this is the first study, at least in the SAARC region, to investigate the non-linear dynamics and causality direction in the twin deficits hypothesis using the MMQR and the JKS causality test.

The study aims to evaluate the influence of capital structure decisions and asset structure on firms' performance for East African listed nonfinancial firms.

The research is descriptive and employs secondary data from the East African capital markets' websites. The generalized method of moments approach is used to estimate the relationship due to its ability to account for endogeneity problems.

The result shows that capital structure decisions and asset structure strongly influence the firms' performance. When long-term debts, short-term debts and tangible fixed assets increase, the return on total assets increases. An increase in the total debt ratio raises the return on equity (ROE). However, the increase in long-term debt lowers the ROE.

The results will help investors and potential investors decide on a financing policy that maximizes performance. Likewise, governments and other policymakers review the capital markets' frameworks to attract institutional and individual investors to the markets for financial availability and to increase profitability.

The research provides evidence on the influence of capital structure decisions and asset structure on firms' performance. Furthermore, its results contribute to firms' financing policy formulation and the corporate finance literature.

This study investigates the determinants of the market capitalization of listed companies through evidence from an emerging country.

This research employs the system generalized method of moments for a dataset of 7,608 observations from 687 Vietnamese listed firms.

Our findings show that both external and internal factors affect market capitalization. Intellectual capital, sales growth, profit, leverage and crises are positively linked to market capitalization; meanwhile, foreign direct investment, inflation and gross domestic product negatively affect market capitalization. The negative effect of macrofactors reflects the fact that the macroeconomic environment can deteriorate investment values and then market capitalization. This implies that macroeconomic stability is very crucial for firms and financial stability. The COVID-19 and financial crisis have a moderating influence on market capitalization through sales growth, profitability and leverage. Unlike previous studies, we find that intellectual capital plays a very essential role regardless of whether there is a crisis or not. Therefore, firms should focus on intellectual capital to grow market capitalization sustainably.

This paper contributes to the literature of market capitalization by investigating the determinants of market capitalization with a joint assessment of the financial crisis and the COVID-19 pandemic, which have not yet been considered together in previous studies. It enriches the literature by investigating the moderating effect of COVID-19 and financial crisis on the relationships between some key determinants and market capitalization. Unlike previous studies, our study highlights the essential role of intellectual capital in enhancing market capitalization regardless of whether there is a crisis.

This chapter reviews the econometric approaches typically used to deal with the spike of zeros when modelling non-negative outcomes such as expenditures, income, or consumption. Relying on the assumptions of selection on observables for evaluating a policy or treatment, this chapter discusses other issues that arise with spikes of zeros in the data, including the analyst's choice between full information versus quasi-likelihood methods, considering whether observed zeros are true or masking more complex behavioural decisions, and dealing with zeros that arise due to self-selection. This chapter ends with discussions of empirical strategies to deal with these behavioural assumptions and a brief review of the literature where such strategies were employed.

The main objective of this article is to analyze the role of governance quality in influencing the economic growth of 22 selected Sub-Saharan African Countries.

The study applied the panel dynamic Generalized Method of Moments (GMM) to analyze the data obtained from the World Bank database over the period from 2002 to 2020.

The overall finding indicated that the composite governance index has a positive significant effect on the economic growth of the countries; where a unit improvement in the aggregate governance index leads to a 3.05% increase in GDP. The disaggregated result has shown that corruption control and government effectiveness have a negative significant effect on growth performance, whereas, the rule of law and regulatory quality showed a positive significant effect. Political stability and voice and accountability have an insignificant effect on economic growth.

Due to data limitations, this study could not address the whole members of Sub Sahara African Countries and could not see the causal relationship.

The study suggested a strong commitment to the implementation of policy and reform measures on all governance factors. This may add to the need to devise participatory corruption control mechanisms; to closely look at the proper implementation of policies and reforms that constitute the government effectiveness factors, and properly implement the rule of law at all levels of the government with a strong commitment to realizing it so that citizens at all levels can have full confidence in and abide by the rules of society.

Even though there are some studies conducted using conventional methods of panel data analysis such as random effect or fixed effects, this empirical study used more advanced panel dynamic generalized moment of methods to examine the role of improvement in governance quality on economic growth.

The purpose of this study is to examine the impact of green bonds on common prosperity in China. Green bonds have gained significant attention as a means to address financial challenges and promote environmental protection. This research aims to investigate the influence of green bonds on common prosperity by utilizing the system-generalized method of moments (SYS-GMM) and analyzing panel data from prefecture-level cities. The study also explores the theoretical mechanisms and heterogeneous relationships between green bonds and common prosperity, providing valuable guidance for advancing economic and social well-being in China.

This study employs a system-generalized method of moments (SYS-GMM) as the methodology to investigate the influence of green bonds on common prosperity in China. Panel data from prefecture-level cities for the period 2014 to 2020 are utilized for analysis. The SYS-GMM approach allows for the examination of dynamic relationships and control of endogeneity issues. By utilizing this methodology, the study aims to provide robust and reliable findings on the impact of green bonds on common prosperity, considering the specific context of China's ecological civilization development and financial challenges faced by energy-saving and environmental protection enterprises.

The findings of this research indicate several important outcomes. Firstly, common prosperity in China experienced substantial growth between 2014 and 2020. Secondly, green bonds have demonstrated a clear and positive impact on common prosperity. They contribute to the enhancement of common prosperity by driving industrial structure upgrading and fostering green technology innovation. Lastly, the study reveals that the positive influence of green bonds on common prosperity is particularly pronounced in the western region of China. These findings highlight the significance of green bonds in promoting sustainable economic development and societal well-being.

This study contributes to the existing literature by examining the impact of green bonds on common prosperity in China, utilizing the system-generalized method of moments (SYS-GMM) and panel data analysis. The research not only adds to the understanding of the relationship between green bonds and economic well-being but also provides insights into the theoretical mechanisms and heterogeneous relationships involved. The findings showcase the positive influence of green bonds on common prosperity, emphasizing their role in addressing financial challenges, promoting environmental protection, and driving sustainable development. The study's conclusions offer valuable guidance for policymakers, financial institutions, and stakeholders in advancing common prosperity in China.