Uncertainty of distributed photovoltaic(PV) power brings great challenges to the safe and stable operation of power system, in which the intermittency problem is more challenging than the fluctuation. This paper focuses on the intermittency problem of distributed PV power, firstly, an intermittency evaluation method based on generalized extreme value(GEV) theory is proposed to solve the problem of the lack of \"small-sample big-gap\" events. Secondly, focusing on high risk events such as high-frequency and warning mutation events, probabilistic evaluation indexes were established, including T-hour-period mutation intensity and T-hour-period mutation frequency. Finally, a two-dimensional joint probability distribution of intermittency elements is established, and the concepts of return period and return level are introduced into the photovoltaic field to provide data support for the configuration of energy storage capacity and duration, and to provide auxiliary decision-making for the execution time and development cycle of interactive projects. The proposed method provides a solution for intermittency evaluation in small sample status quo with strong data compatibility and engineering replicability.

UNASSIGNED: This study examines the impact of socioeconomic factors on calorie intake and macronutrient composition at the household level in Pakistan from 2006 to 2016, using data from the Household Integrated Income and Consumption Survey (HIICS). By applying a copula-based decomposition method, it identifies key drivers such as urbanization, household size, paternal education, income, and cultivation, highlighting their roles in dietary changes and implications for public health. The findings are crucial for understanding nutritional shifts and addressing non-communicable diseases.
UNASSIGNED: This study was conducted to assess the socioeconomic changes in total calorie intake per capita and calories obtained from macronutrients (fat, protein, and carbohydrates) at the household level in Pakistan.
UNASSIGNED: : Cross-sectional data were taken from 2 national-level surveys published by the Pakistan Bureau of Statistics: the Household Integrated Economic Survey 2006 (14,948 households) and the Household Integrated Income and Consumption Survey 2016 (7842 households). Participants were from all 4 provinces of Pakistan. A copula-based decomposition method was applied to decompose the 10-y change in the distribution (mean, median, and quartiles) of the total calorie intake per capita and calories obtained from macronutrients.
UNASSIGNED: The estimated results of decomposition revealed that total calorie intake per capita has increased on average and in the considered quartiles. The calories obtained from fat and carbohydrates have increased, whereas calories from protein have decreased, according to the distribution of the mean and quartile. The composition effect was negative for all outcome variables, and the main drivers of the composition effect were urbanization, household size, paternal education, income, and cultivation for all outcome variables.
UNASSIGNED: Household size and income are the most important covariates in an increase of total calories per capita and consumption of macronutrients, but urbanization, paternal education, and cultivation contribute negatively to the composition effect. Such findings are very important to inform researchers about nutritional change at the national level because the correlation between dietary change and risk factors for noncommunicable diseases such as heart disease and obesity is very strong.

The increasingly frequent occurrence of urban heatwaves has become a significant threat to human health. To quantitatively analyze changes in heatwave characteristics and to investigate the return periods of future heatwaves in Wuhan City, China, this study extracted 9 heatwave definitions and divided them into 3 mortality risk levels to identify and analyze historical observations and future projections of heatwaves. The copula functions were employed to derive the joint distribution of heatwave severity and duration and to analyze the co-occurrence return periods. The results demonstrate the following. (1) As the concentration of greenhouse gas emissions increases, the severity of heatwaves intensifies, and the occurrence of heatwaves increases significantly; moreover, a longer duration of heatwaves correlated with higher risk levels in each emission scenario. (2) Increasing concentrations of greenhouse gas emissions result in significantly shorter heatwave co-occurrence return periods at each level of risk. (3) In the 3 risk levels under each emission scenario, the co-occurrence return periods for heatwaves become longer as heatwave severity intensifies and duration increases. Under the influence of climate change, regional-specific early warning systems for heatwaves are necessary and crucial for policymakers to reduce heat-related mortality risks in the population, especially among vulnerable groups.

Vibrational environments can cause drift or changes in Micro-Electro-Mechanical System (MEMS) gyroscope rotor parameters, potentially impacting their performance. To improve the effective use of MEMS gyroscopes, this study introduced a method for evaluating the reliability of parameter degradation under vibration. We analyzed the working principle of MEMS gyroscope rotors and investigated how vibration affects their parameters. Focusing on zero bias and scale factor as key performance indicators, we developed an accelerated degradation model using the distributional assumption method. We then collected degradation data for these parameters under various vibration conditions. Using the Copula function, we established a reliability assessment approach to evaluate the degradation of the MEMS gyroscope rotor\'s zero bias and scale factor under vibration, enabling the determination of reliability for these parameters. Experimental findings confirmed that increasing stress levels lead to reduced failure times and increased failure rates for MEMS gyroscope rotors, with significant changes observed in the zero bias parameter. Our evaluation method effectively characterizes changes in the reliability of the MEMS gyroscope rotor\'s scale factor and zero bias over time, providing valuable information for practical applications of MEMS gyroscopes.

Chongqing, as the last ecological barrier of the Upper Yangtze River, is constrained to achieve \"dual carbon\" goals due to imbalanced energy structure. Based on selecting the energy structure influencing factors through Copula function and Granger causality, a multi-dimensional dynamic support vector machine model (SSA-MFD-SVR-ARIMA) by adopting sparrow algorithm was constructed to predict the proportion of Chongqing\'s energy structure from 2021 to 2030 under the drive of green finance development, and an optimization path was obtained. The novel findings confirm that (1) the correlated contribution rate of Green Finance to optimizing Chongqing\'s Energy Structure is 10.8 %; (2) under the sustained growth rate of Green Finance at 4.5 %, the proportion of coal consumption will reach 40.03 % by 2030, and non-fossil energy consumption will account for 27 %. It confirms that Chongqing can achieve the Energy Development Plan assigned by the Central Government in 2025. The research proposes a four-dimensional optimized pathway from a financial perspective that includes green equity investments, digital finance for energy, financing environmental rights and interests, and developing an industry fund. Furthermore, our put forward the safeguard strategies for financing, innovation, linkage, and protection mechanisms of this pathway optimization.

Droughts are widespread in China and have brought considerable losses to the economy and society. Droughts are intricate, stochastic processes with multi-attributes (e.g., duration, severity, intensity, and return period). However, most drought assessments tend to focus on univariate drought characteristics, which are inadequate to describe the intrinsic characteristics of droughts due to the existence of correlations between drought attributes. In this study, we employed the standardized precipitation index to identify drought events using China\'s monthly gridded precipitation dataset from 1961 to 2020. Univariate and copula-based bivariate methods were then used to examine drought duration and severity on 3-, 6-, and 12-month time scales. Finally, we used the hierarchical cluster method to identify drought-prone regions in mainland China at various return periods. Results revealed that time scale played an essential role in the spatial heterogeneity of drought behaviors, such as average characteristics, joint probability, and risk regionalization. The main findings were as follows: (1) 3- and 6-month time scales yielded comparable regional drought features, but not 12-month time scales; (2) higher drought severity was associated with longer drought duration; (3) drought risk was higher in the northern Xinjiang, western Qinghai, southern Tibet, southwest China, and the middle and lower reaches of the Yangtze River, and lower in the southeastern coastal areas of China, the Changbai Mountains, and the Greater Khingan Mountains; (4) mainland China was divided into six subregions according to joint probabilities of drought duration and severity. Our study is expected to contribute to better drought risk assessment in mainland China.

In multivariate longitudinal studies, several outcomes are repeatedly measured for each subject over time. The data structure of these studies creates two types of associations which should take into account by the model: association of outcomes at a given time point and association among repeated measurements over time for a specific outcome. In our approach, because of some advantageous arisen from features like flexibility of marginal distributions, a copula-based approach is used for joint modeling of multivariate outcomes at each time points, also a transition model is used for considering the association of longitudinal measurements over time. For the problem of incomplete data, missingness mechanism is assumed to be ignorable. Some simulation results are reported in different scenarios using the Gaussian, t and several commonly used copulas of the family of Archimedean copulas. Akaike information criterion (AIC) is used to select the best copula function. The proposed approach is also used for analyzing a real obesity data set.

Temperature and precipitation are the two most critical climate variables and their extreme states have more severe impacts than average states on both human society and natural ecosystem. In this study, an integrated multivariate trend-frequency analysis (IMTFA) approach is developed for the risk assessment of climate extremes under the global warming. Through incorporating multiple time series analysis techniques (i.e., M-K test, Sen\'s slope estimator and Pettitt test) and copula function into a general framework, IMTFA is capable not only of analyzing the temporal trends and change points of extreme temperatures and precipitations, but also of quantifying their univariate and multivariate risks. IMTFA is applied to the Central Asia with considering a long-term (1881-2018) observation data. Our findings are: (i) significant wetting and warming trends were occurred in the Central Asia over past one hundred years, where 42.5%, 59.4% and 79.2% stations have change points for extreme precipitations, maximum and minimum temperatures, respectively; (ii) the occurrences of extreme climate events show obviously spatial heterogeneity, where the highest risks of meteorological drought, flood and frost events are occurred in the southwest, southeast and northeast regions, respectively; (iii) global warming significantly affects the intensities and frequencies of extreme precipitations and temperatures, and their univariate and multivariate risks are intensified in the most regions of Central Asia. The above findings can provide more valuable information for risk assessment and disaster adaptation of climate extremes in Central Asia.

Wave height and wave period are important oceanic environmental factors that are used to describe the randomness of a wave. Within the field of ocean engineering, the calculation of design wave height is of great significance. In this paper, a periodic maximum entropy distribution function with four undetermined parameters is derived by means of coordinate transformation and solving conditional variational problems. A double entropy joint distribution function of wave height and wave period is also derived. The function is derived from the maximum entropy wave height function and the maximum entropy periodic function, with the help of structures of the Copula function. The double entropy joint distribution function of wave height and wave period is not limited by weak nonlinearity, nor by normal stochastic process and narrow spectrum. Besides, it can fit the observed data more carefully and be more widely applicable to nonlinear waves in various cases, owing to the many undetermined parameters it contains. The engineering cases show that the recurrence level derived from the double entropy joint distribution function is higher than that from the extreme value distribution using the single variables of wave height or wave period. It is also higher than that from the traditional joint distribution function of wave height and wave period.

We develop an empirical likelihood approach to test independence of two univariate random variables X and Y versus the alternative that X and Y are strictly positive quadrant dependent (PQD). Establishing this type of ordering between X and Y is of interest in many applications, including finance, insurance, engineering, and other areas. Adopting the framework in Einmahl and McKeague (2003, Bernoulli), we create a distribution-free test statistic that integrates a localized empirical likelihood ratio test statistic with respect to the empirical joint distribution of X and Y. When compared to well known existing tests and distance-based tests we develop by using copula functions, simulation results show the EL testing procedure performs well in a variety of scenarios when X and Y are strictly PQD. We use three data sets for illustration and provide an online R resource practitioners can use to implement the methods in this article.