Industrial green technology innovation has become an important content in achieving high-quality economic growth and comprehensively practicing the new development concept in the new era. This paper measures the efficiency of industrial green technology innovation and regional differences based on Chinese provincial panel data from 2005 to 2018, using a combination of the super-efficient SBM model for considering undesirable outputs and the Dagum Gini coefficient method, and discusses and analyses the factors influencing of the industrial green technology innovation efficiency by constructing a spatial econometric model. The results show that: firstly, the industrial green technology innovation efficiency in China shows a relatively stable development trend, going through three stages: " stationary period", " recession period " and "growth period ". However, the efficiency gap between different regions is obvious, specifically in the eastern > central > western regions of China, and the industrial green technology efficiency innovation in the central and western regions is lower than the national average. Secondly, regional differences in the efficiency of industrial green technology innovation in China are evident but tend to narrow overall, with the main reason for the overall difference being regional differences. In terms of intra-regional variation, variation within the eastern region is relatively stable, variation within the central region is relatively low and shows an inverted 'U' shaped trend, and variation within the western region is high and shows a fluctuating downward trend. Thirdly, the firm size, government support, openness to the outside world, environmental regulations and education levels contribute to the efficiency of industrial green technology innovation. In addition, the industrial structure hinders the efficiency of industrial green technology innovation, and each influencing factor has different degrees of spatial spillover effects.

Developments of new probability models for data analysis are keen interest of importance for all fields. The log-Dagum distribution has a prominent role in the theory and practice of statistics. In this article, a new family of continuous distributions generated from a log Dagum random variable called the log-Dagum Weibull distribution is proposed. The key properties of the proposed distribution are derived. Its density function can be symmetrical, left-skewed, right-skewed and reversed-J shaped and can have increasing, decreasing, bathtub hazard rates shaped. The model parameters are estimated by the method of maximum likelihood and illustrate its importance by means of applications to real data sets.

In the paper, we measure the digital financial inclusion index of 31 provinces in China from 2011 to 2020 based on three dimensions: coverage breadth, depth of use and digitalization degree. By means of weighted Dagum Gini coefficient and quantile standardization, we explored the degree of imbalance and insufficiency of the development of digital inclusive finance in China and four major regions and its structural causes. Using Kernel density estimation method and Markov chain analysis method, we further investigates the evolution trend of imbalance and insufficiency. The study finds that (1) the Digital Inclusive Financial Index in China and the four major regions rise significantly, with the COVID-19 epidemic reducing its growth rate. Of these, the eastern region has the highest development level. (2) The imbalance level of digital inclusive finance development obviously has reduced. The level of imbalance is highest within the eastern region, and the development gap between the eastern and western regions is the widest. The imbalance of overall development is mainly due to the regional imbalance. The imbalance of coverage breadth and depth of use is the main structural cause of unbalanced development in the four major regions. There is a trend of bipolarization or multipolarization in China and the other three major regions, with the exception of the central region. (3) The western region is the least developed. The development shortcoming of digital inclusive finance in China and the four major regions is the breadth of coverage. There are "Club Convergence" and "Matthew Effect" in the eastern, central and western regions.

Smart City has emerged as the mainstream paradigm for urban governance innovation, sustainable development, and strategy upgrades, which is drawing attention from scholars worldwide. However, current frameworks for Smart City assessment remain incomplete and simplistic. In is paper, 30 national or provincial capitals in China were selected and we designed a tri-dimensional SPI model—Social, Physical, and Information Space—for smart city spatial development assessment. Utilizing methods such as entropy weighting, coupled coordination degree models, and the Dagum Gini coefficient, this study assesses the spatial development and coupled coordination of 30 cities from 2011 to 2019. Finally, by means of BP neural networks, the study examines the contribution of each indicator to the spatial coupled coordination. The results indicated that with a narrowing disparity in development speeds among different regions, the spatial coupled coordination development level of smart capitals in China has steadily increased, presenting a pattern of staggered distribution. Moreover, the IS subsystem plays the most significant role in coupled coordination. The significance of this research lies in its tri-dimensional spatial perspective of the spatial development and coupled coordination differences of the Smart City, providing evidence-based support for the regional layout and optimization in China.