In the vast statistical literature, there are numerous probability distribution models that can model data from real-world phenomena. New probability models, nevertheless, are still required in order to represent data with various spread behaviors. It is a known fact that there is a great need for new models with limited support. In this study, a flexible probability model called the unit Maxwell-Boltzmann distribution, which can model data values in the unit interval, is derived by selecting the Maxwell-Boltzmann distribution as a base-line model. The important characteristics of the derived distribution in terms of statistics and mathematics are investigated in detail in this study. Furthermore, the inference problem for the mentioned distribution is addressed from the perspectives of maximum likelihood, method of moments, least squares, and maximum product space, and different estimators are obtained for the unknown parameter of the distribution. The derived distribution outperforms competitive models according to different fit tests and information criteria in the applications performed on four actual air pollutant concentration data sets, indicating that it is an effective model for modeling air pollutant concentration data.

Accurate forecasting of claim frequency in automobile insurance is essential for insurers to assess risks effectively and establish appropriate pricing policies. Traditional methods typically rely on a Poisson distribution for modeling claim counts; however, this approach can be inadequate due to frequent zero-claim periods, leading to zero inflation in the data. Zero inflation occurs when more zeros are observed than expected under standard Poisson or negative binomial (NB) models. While machine learning (ML) techniques have been explored for predictive analytics in other contexts, their application to zero-inflated insurance data remains limited. This study investigates the utility of ML in improving forecast accuracy under conditions of zero-inflation, a data characteristic common in automobile insurance. The research involved a comparative evaluation of several models, including Poisson, NB, zero-inflated Poisson (ZIP), hurdle Poisson, zero-inflated negative binomial (ZINB), hurdle negative binomial, random forest (RF), support vector machine (SVM), and artificial neural network (ANN) on an insurance dataset. The performance of these models was assessed using mean absolute error. The results reveal that the SVM model outperforms others in predictive accuracy, particularly in handling zero-inflation, followed by the ZIP and ZINB models. In contrast, the traditional Poisson and NB models showed lower predictive capabilities. By addressing the challenge of zero-inflation in automobile claim data, this study offers insights into improving the accuracy of claim frequency predictions. Although this study is based on a single dataset, the findings provide valuable perspectives on enhancing prediction accuracy and improving risk management practices in the insurance industry.

The direct estimation of soil hydraulic conductivity (Ks) requires expensive laboratory measurement to present adequately soil properties in an area of interest. Moreover, the estimation process is labor and time-intensive due to the difficulties of collecting the soil samples from the field. Hence, innovative methods, such as machine learning techniques, can be an alternative to estimate Ks. This might facilitate agricultural water and nutrient management which has an impact on food and water security. In this spirit, the study presents neural-network-based models (artificial neural network (ANN), deep learning (DL)), tree-based (decision tree (DT), and random forest (RF)) to estimate Ks using eight combinations of soil data under calcareous alluvial soils in a semi-arid region. The combinations consisted of soil data such as clay, silt, sand, porosity, effective porosity, field capacity, permanent wilting point, bulk density, and organic carbon contents. The results compared with the well-established model showed that all the models had satisfactory results for the estimation of Ks, where ANN7 with soil inputs of sand, silt, clay, permanent wilting point, field capacity, and bulk density values showed the best performance with mean absolute error (MAE) of 2.401 mm h⁻¹, root means square error (RMSE) of 3.096 mm h⁻¹, coefficient of determination (R²) of 0.940, and correlation coefficient (CC) of 0.970. Therefore, the ANN could be suggested among the neural-network-based models. Otherwise, RF could also be used for the estimation of Ks among the tree-based models.

Financial markets are increasingly interlinked. Therefore, this study explores the complex relationships between the Tadawul All Share Index (TASI), West Texas Intermediate (WTI) crude oil prices, and Bitcoin (BTC) returns, which are pivotal to informed investment and risk-management decisions. Using copula-based models, this study identified Student’s t copula as the most appropriate one for encapsulating the dependencies between TASI and BTC and between TASI and WTI prices, highlighting significant tail dependencies. For the BTC–WTI relationship, the Frank copula was found to have the best fit, indicating nonlinear correlation without tail dependence. The predictive power of the identified copulas were compared to that of Long Short-Term Memory (LSTM) networks. The LSTM models demonstrated markedly lower Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Scaled Error (MASE) across all assets, indicating higher predictive accuracy. The empirical findings of this research provide valuable insights for financial market participants and contribute to the literature on asset relationship modeling. By revealing the most effective copulas for different asset pairs and establishing the robust forecasting capabilities of LSTM networks, this paper sets the stage for future investigations of the predictive modeling of financial time-series data. The study highlights the potential of integrating machine-learning techniques with traditional econometric models to improve investment strategies and risk-management practices.

Unit distributions, exhibiting inherent symmetrical properties, have been extensively studied across various fields. A significant challenge in these studies, particularly evident in parameter estimations, is the existence and uniqueness of estimators. Often, it is challenging to demonstrate the existence of a unique estimator. The major issue with maximum likelihood and other estimator-finding methods that use iterative methods is that they need an initial value to reach the solution. This dependency on initial values can lead to local extremes that fail to represent the global extremities, highlighting a lack of symmetry in solution robustness. This study applies a very simple, and unique, estimation method for unit Weibull and unit Burr XII distributions that both attain the global maximum value. Therefore, we can conclude that the findings from the obtained propositions demonstrate that both the maximum likelihood and graphical methods are symmetrically similar. In addition, three real-world data applications are made to show that the method works efficiently.

This study examined the performance of random forest (RF), support vector machine (SVM) and adaptive boosting (AB) machine learning models used to estimate daily potato crop evapotranspiration adjusted (ET_c-adj) under full irrigation (I₁₀₀), 50% of full irrigation supply (I₅₀) and rainfed cultivation (I₀). Five scenarios of weather, crop and soil data availability were considered: (S1) reference evapotranspiration and precipitation, (S2) S1 and crop coefficient, (S3) S2, the fraction of total available water and root depth, (S4) S2 and total soil available water, and (S5) S3 and total soil available water. The performance of machine learning models was compared with the standard FAO56 calculation procedure. The most accurate ET_c-adj estimates were observed with AB4 for I₁₀₀, RF3 for I₅₀ and AB5 for I₀ with coefficients of determination (R²) of 0.992, 0.816 and 0.922, slopes of 1.004, 0.999 and 0.972, modelling efficiencies (EF) of 0.992, 0.815 and 0.917, mean absolute errors (MAE) of 0.125, 0.405 and 0.241 mm day⁻¹, root mean square errors (RMSE) of 0.171, 0.579 and 0.359 mm day⁻¹ and mean squared errors (MSE) of 0.029, 0.335 and 0.129 mm day⁻¹, respectively. The AB model is suggested for ET_c-adj prediction under I₁₀₀ and I₀ conditions, while the RF model is recommended under the I₅₀ condition.