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Recently, bounded distributions have attracted attention. These distributions are frequently used in modeling rate and proportion data sets. In this study, a new alternative model is proposed for modeling bounded data sets. Parameter estimations of the proposed distribution are obtained via maximum likelihood method. In addition, a new regression model is defined under the proposed distribution and its residual analysis is examined. As a result of the empirical studies on real data sets, it is observed that the proposed regression model gives better results than the unit-Weibull and Kumaraswamy regression models.

Focusing on the key air pollution regions in China by using hourly automatic weather data, ground-based and high-altitude meteorological sounding data, and near-surface O 3 monitoring data, here, we try to quantify the relationship between boundary layer meteorological condition and near-surface O 3 concentrations. The key meteorological element includes changes in solar zenith angle, cloud height, atmospheric condensation rate, and the associated change in the boundary layer height. We also try to better understand the mechanisms by which meteorological conditions affect near-surface O 3 concentrations, and it is found that the exponential increase in near-surface O 3 concentrations after sunrise (called the O 3 concentration entrainment, EZ) is meaningfully associated with exceeding the threshold of a water vapor condensation rate ( f c ) that is often closely linked to a significant rise in the pollution boundary layer and that this proves to be diagnostically important for understanding the O 3 EZ. Diurnal variations in solar zenith angle and boundary layer height are key meteorological factors influencing the large increase in near-surface O 3 concentration entrainment.

Interpolation sequences in the Pavlov–Korevaar–Dixon sense and their generalizations are studied. The relationship between Macintyre sequences, convergence class, and interpolation sequences is discussed. Interpolation sequences have the property that the corresponding systems of powers (exponential systems) form strongly incomplete and strongly free (minimal) systems. The issues of interpolation of sequences of natural numbers, as well as symmetric sequences of integers, have been studied to some extent in the works of J. Korevaar and M. Dixon. However, they generally failed to characterize them, but limited themselves to considering particular examples (Pavlov and Kovari sequences). Later, B. Berndtsson succeeded in proving the interpolation criterion for sequences of natural numbers. R.A. Gaisin proved a similar criterion for arbitrary positive sequences in a broader class of entire functions defined by the majorant of the convergence class. Later, he also proved the corresponding criterion for symmetric sequences of real numbers. In this article, the Pavlov–Korevaar–Dixon type interpolation criterion for arbitrary real nodes is proved.

This research proposes and evaluates the effectiveness of the Alpha‐Logarithmic Power Transformed Exponential (ALPTE) distribution as a more general‐purpose, versatile lifetime distribution in comparison to conventional lifetime distributions. Bayesian and non‐Bayesian estimation were studied along with some properties of the ALPTE model, which were discussed. Mortality, Mobility, and Radiation datasets were analyzed and compared in a detailed manner. Data was evaluated using maximum likelihood estimation, descriptive statistics, and the goodness‐of‐fit tests such as AIC, BIC, CAIC, HQIC, Kolmogorov‐Smirnov, Anderson‐Darling, Cramér‐von Mises, and analyzed visually through model diagnostic plots such as boxplots, TTT plots, and P‐P plots. The ALPTE model consistently demonstrated superior performance over the Gamma, Lognormal, Gumbel, Weibull, and Exponential models across all datasets. It is remarkable how the ALPTE model not only enhanced the representation of light‐ and heavy‐tailed phenomena but also exhibited robustness to outliers alongside multiplicity in failure patterns, including increases, decreases, or constant rates. Estimates of ALPTE remained robust and interpretable even in the presence of data heterogeneity, particularly in large sample sizes. Such claims of flexibility and versatility further highlight the adaptability of the ALPTE distribution. The Alpha‐Logarithmic Power Transformed Exponential (ALPTE) distribution is introduced as a highly versatile lifetime model, demonstrating superior goodness‐of‐fit over common distributions (e.g., Gamma, Weibull) across diverse datasets. Its robust performance, even with data heterogeneity and outliers, showcases its adaptability for modeling various failure patterns and tail behaviors.

1. Dispersal is fundamental to ecological processes at all scales and levels of organization, but progress is limited by a lack of information about the general shape and form of plant dispersal kernels. We addressed this gap by synthesizing empirical data describing seed dispersal and fitting general dispersal kernels representing major plant types and dispersal modes. 2. A comprehensive literature search resulted in 107 papers describing 168 dispersal kernels for 144 vascular plant species. The data covered 63 families, all the continents except Antarctica, and the broad vegetation types of forest, grassland, shrubland and more open habitats (e.g. deserts). We classified kernels in terms of dispersal mode (ant, ballistic, rodent, vertebrates other than rodents, vehicle or wind), plant growth form (climber, graminoid, herb, shrub or tree), seed mass and plant height. 3. We fitted 11 widely used probability density functions to each of the 168 data sets to provide a statistical description of the dispersal kernel. The exponential power (ExP) and log-sech (LogS) functions performed best. Other 2-parameter functions varied in performance. For example, the log-normal and Weibull performed poorly, while the 2Dt and power law performed moderately well. Of the single-parameter functions, the Gaussian performed very poorly, while the exponential performed better. No function was among the best-fitting for all data sets. 4. For 10 plant growth form/dispersal mode combinations for which we had >3 data sets, we fitted ExP and LogS functions across multiple data sets to provide generalized dispersal kernels. We also fitted these functions to subdivisions of these growth form/dispersal mode combinations in terms of seed mass (for animal-dispersed seeds) or plant height (wind-dispersed) classes. These functions provided generally good fits to the grouped data sets, despite variation in empirical methods, local conditions, vegetation type and the exact dispersal process. 5. Synthesis. We synthesize the rich empirical information on seed dispersal distances to provide standardized dispersal kernels for 168 case studies and generalized kernels for plant growth form/dispersal mode combinations. Potential uses include the following: (i) choosing appropriate dispersal functions in mathematical models; (ii) selecting informative dispersal kernels for one's empirical study system; and (iii) using representative dispersal kernels in cross-taxon comparative studies.

We discuss a special class of generalized divergence measures by the use of generator functions. Any divergence measure in the class is separated into the difference between cross and diagonal entropy. The diagonal entropy measure in the class associates with a model of maximum entropy distributions; the divergence measure leads to statistical estimation via minimization, for arbitrarily giving a statistical model. The dualistic relationship between the maximum entropy model and the minimum divergence estimation is explored in the framework of information geometry. The model of maximum entropy distributions is characterized to be totally geodesic with respect to the linear connection associated with the divergence. A natural extension for the classical theory for the maximum likelihood method under the maximum entropy model in terms of the Boltzmann-Gibbs-Shannon entropy is given. We discuss the duality in detail for Tsallis entropy as a typical example.

Aim The spatio‐temporal distribution of biodiversity is a core field of biogeography, and the so‐termed species–time–area relationship (STAR), together with its siblings, that is the SAR (species–area relationship) and STR (species–time relationship), has achieved the rare status of classic laws in ecology and biogeography. Traditionally, the STAR or its recent generalization DTAR (diversity–time–area relationship) has been described with the bivariate power law (BPL) model or more recently with Whittaker, Triantis, and Ladle (2008, Journal of Biography; 35: 18) general dynamic model (GDM). We propose to extend the classic BPL into a more flexible DTAR model, which offers new quantitative methods for estimating maximal global diversity and charactering the relationship between local and regional diversity. Location Indoor microbiome. Taxon Microbes. Method We revise the BPL model by introducing two taper‐off (cut‐off) parameters or BPLEC (bivariate power law with exponential cutoffs) model, which eventually overwhelms the unsaturated increase of diversity over time and/or space and consequently can offer more realistic modelling of the joint spatio‐temporal distribution of biodiversity. Based on the BPLEC model, we further define three new concepts for DTAR: maximal accrual diversity (MAD) profile, local‐to‐regional diversity (LRD) ratio profile and local‐to‐global diversity (LGD) ratio profile. Results We introduce and demonstrate the new BPLEC model with the indoor microbiome datasets (Lax et al., 2014, Science; 345: 1048–1052). The new model fitted to the microbiome datasets equally well or slightly better than existing BPL and GDM models, but it possesses two advantages stated below. Main conclusion First, the new BPLEC model overcomes the unlimited diversity accrual in temporal and/or spatial dimensions and hence offers more realistic modelling to the DTAR. Second, the MAD and LRD/LGD offer useful methods for estimating the “dark” or “potential” diversity, which accounts for the species locally absent but present in a habitat‐specific regional species pool.

Progressive-stress accelerated life testing (PSALT) is a specialized experimental method that evaluates the longevity of a product under continuously fluctuating stress levels. Due to the constraints of testing equipment and expenses, the lifetime data collected by PSALT are typically censored. This paper introduces the PSALT model that utilizes Type-II unified progressive hybrid censoring to address this data characteristic, specifically when the lifespan of test units follows a truncated Cauchy power exponential (TCPE) distribution. The distribution’s scale parameter follows the inverse power law, and the cumulative exposure model is relevant for the effects of differing stress levels. The estimation methods for the TCPE parameters and the acceleration factor are examined, including maximum likelihood and Bayesian estimation techniques. Bayesian estimates are generated using the Markov chain Monte Carlo technique based on symmetric and asymmetric loss functions. The highest posterior density intervals are assessed, as well as asymptotic confidence intervals. A simulation study is conducted to evaluate the efficacy of the proposed point and interval estimators. Ultimately, a real data set is applied to the TCPE distribution, and the proposed estimators are assessed.

Satellite Interferometric Synthetic Aperture Radar (InSAR) is widely used for topographic, geological and natural resource investigations. However, most of the existing InSAR studies of ground deformation are based on relatively short periods and single sensors. This paper introduces a new multi-sensor InSAR time series data fusion method for time-overlapping and time-interval datasets, to address cases when partial overlaps and/or temporal gaps exist. A new Power Exponential Knothe Model (PEKM) fits and fuses overlaps in the deformation curves, while a Long Short-Term Memory (LSTM) neural network predicts and fuses any temporal gaps in the series. Taking the city of Wuhan (China) as experiment area, COSMO-SkyMed (2011-2015), TerraSAR-X (2015-2019) and Sentinel-1 (2019-2021) SAR datasets were fused to map long-term surface deformation over the last decade. An independent 2011-2020 InSAR time series analysis based on 230 COSMO-SkyMed scenes was also used as reference for comparison. The correlation coefficient between the results of the fusion algorithm and the reference data is 0.87 in the time overlapping region and 0.97 in the time-interval dataset. The correlation coefficient of the overall results is 0.78, which fully demonstrates that the algorithm proposed in our paper achieves a similar trend as the reference deformation curve. The experimental results are consistent with existing studies of surface deformation at Wuhan, demonstrating the accuracy of the proposed new fusion method to provide robust time series for the analysis of long-term land subsidence mechanisms.

In short-range microwave imaging, the collection of data in real environments for the purpose of developing techniques for target detection is very cumbersome. Simultaneously, to develop effective and efficient AI/ML-based techniques for target detection, a sufficiently large dataset is required. Therefore, to complement labor-intensive and tedious experimental data collected in a real cluttered environment, synthetic data generation via cost-efficient electromagnetic wave propagation simulations is explored in this article. To obtain realistic synthetic data, a 3-D model of an antenna, instead of a point source, is used to include the coupling effects between the antenna and the environment. A novel printed scalable ultra-wide band (UWB) log-periodic antenna with a tapered feed line is designed and incorporated in simulation models. The proposed antenna has a highly directional radiation pattern with considerable high gain (more than 6 dBi) on the entire bandwidth. Synthetic data are generated for two different applications, namely through-the-wall imaging (TWI) and through-the-foliage imaging (TFI). After the generation of synthetic data, clutter removal techniques are also explored, and results are analyzed in different scenarios. Post-analysis shows evidence that the proposed UWB log-periodic antenna-based synthetic imagery is suitable for use as an alternative dataset for TWI and TFI application development, especially in training machine learning models.