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Gross domestic product (GDP) serves as a crucial economic indicator for measuring a country's economic growth, exhibiting both linear and non-linear trends. This study aims to analyze and propose an efficient and accurate time series approach for modeling and forecasting the GDP annual growth rate (%) of Saudi Arabia, a key financial indicator of the country. Stochastic linear and non-linear time series modeling, along with hybrid approaches, are employed and their results are compared. Initially, conventional linear and nonlinear methods such as ARIMA, Exponential smoothing, TBATS, and NNAR are applied. Subsequently, hybrid models combining these individual time series approaches are utilized. Model diagnostics, including mean absolute error (MAE), root mean square error (RMSE), and mean absolute percentage error (MAPE), are employed as criteria for model selection to identify the best-performing model. The findings demonstrated that the neural network autoregressive (NNAR) model, as a non-linear approach, outperformed all other models, exhibiting the lowest values of MAE, RMSE and MAPE. The NNAR(5,3) projected the GDP of 1.3% which is close to the projection of IMF benchmark (1.9) for the year 2023. The selected model can be employed by economists and policymakers to formulate appropriate policies and plans. This quantitative study provides policymakers with a basis for monitoring fluctuations in GDP growth from 2022 to 2029 and ensuring the sustained progression of GDP beyond 2029. Additionally, this study serves as a guide for researchers to test these approaches in different economic dynamics.

A robust generalisation of the Gumbel distribution is proposed in this article. This family of distributions is based on the T-X paradigm. From a list of special distributions that have evolved as a result of this family, three separate models are also mentioned in this article. A linear combination of generalised exponential distributions can be used to characterise the density of a new family, which is critical in assessing some of the family’s properties. The statistical features of this family are determined, including exact formulations for the quantile function, ordinary and incomplete moments, generating function, and order statistics. The model parameters are estimated using the maximum likelihood method. Further, one of the unique models has been systematically studied. Along with conventional skewness measures, MacGillivray skewness is also used to quantify the skewness measure. The new probability distribution also enables us to determine certain critical risk indicators, both numerically and graphically. We use a simulated assessment of the suggested distribution, as well as apply three real-world data sets in modelling the proposed model, in order to ensure its authenticity and superiority.

In this paper, we introduce the exponentiated power generalized Weibull power series (EPGWPS) family of distributions, obtained by compounding the exponentiated power generalized Weibull and power series distributions. By construction, the new family contains a myriad of new flexible lifetime distributions having strong physical interpretations (lifetime system, biological studies…). We discuss the characteristics and properties of the EPGWPS family, including its probability density and hazard rate functions, quantiles, moments, incomplete moments, skewness and kurtosis. The main vocation of the EPGWPS family remains to be applied in a statistical setting, and data analysis in particular. In this regard, we explore the estimation of the model parameters by the maximum likelihood method, with accuracy supported by a detailed simulation study. Then, we apply it to two practical data sets, showing the applicability and competitiveness of the EPGWPS models in comparison to some other well-reputed models.

In recent years, the trigonometric families of continuous distributions have found a place of choice in the theory and practice of statistics, with the Sin-G family as leader. In this paper, we provide some contributions to the subject by introducing a flexible extension of the Sin-G family, called the transformed Sin-G family. It is constructed from a new polynomial-trigonometric function presenting a desirable “versatile concave/convex” property, among others. The modelling possibilities of the former Sin-G family are thus multiplied. This potential is also highlighted by a complete theoretical work, showing stochastic ordering results, studying the analytical properties of the main functions, deriving several kinds of moments, and discussing the reliability parameter as well. Then, the applied side of the proposed family is investigated, with numerical results and applications on the related models. In particular, the estimation of the unknown model parameters is performed through the use of the maximum likelihood method. Then, two real life data sets are analyzed by a new extended Weibull model derived to the considered trigonometric mechanism. We show that it performs the best among seven comparable models, illustrating the importance of the findings.

This study proposes the machine learning based classification of medical plant leaves. The total six varieties of medicinal plant leaves-based dataset are collected from the Department of Agriculture, The Islamia University of Bahawalpur, Pakistan. These plants are commonly named in English as (herbal) Tulsi, Peppermint, Bael, Lemon balm, Catnip, and Stevia and scientifically named in Latin as Ocimum sanctum, Mentha balsamea, Aegle marmelos, Melissa officinalis, Nepeta cataria, and Stevia rebaudiana, respectively. The multispectral and digital image dataset are collected via a computer vision laboratory setup. For the preprocessing step, we crop the region of the leaf and transform it into a gray level format. Secondly, we perform a seed intensity-based edge/line detection utilizing Sobel filter and draw five regions of observations. A total of 65 fused features dataset is extracted, being a combination of texture, run-length matrix, and multi-spectral features. For the feature optimization process, we employ a chi-square feature selection approach and select 14 optimized features. Finally, five machine learning classifiers named as a multi-layer perceptron, logit-boost, bagging, random forest, and simple logistic are deployed on an optimized medicinal plant leaves dataset, and it is observed that the multi-layer perceptron classifier shows a relatively promising accuracy of 99.01% as compared to the competition. The distinct classification accuracy by the multi-layer perceptron classifier on six medicinal plant leaves are 99.10% for Tulsi, 99.80% for Peppermint, 98.40% for Bael, 99.90% for Lemon balm, 98.40% for Catnip, and 99.20% for Stevia.

In this study, we have presented a novel probabilistic model called the neutrosophic Burr-III distribution, designed for applications in neutrosophic surface analysis. Neutrosophic analysis allows for the incorporation of vague and imprecise information, reflecting the reality that many real-world problems involve ambiguous data. This ability to handle vagueness can lead to more robust and realistic models especially in situation where classical models fall short. We have also explored the neutrosophic Burr-III distribution in order to deal with the ambiguity and vagueness in the data where the classical Burr-III distribution falls short. This distribution offers valuable insights into various reliability properties, moment expressions, order statistics, and entropy measures, making it a versatile tool for analyzing complex data. To assess the practical relevance of our proposed distribution, we applied it to real-world data sets and compared its performance against the classical Burr-III distribution. The findings revealed that the neutrosophic Burr-III distribution outperformed than the classical Burr-III distribution in capturing the underlying data characteristics, highlighting its potential as a superior modeling toolin various fields.

The main focus of this paper is to introduce a new probability model. Specifically, this paper presents a modified form of the Weibull distribution and investigates its various statistical properties, such as moments, moment-generating functions, reliability functions, quantile functions, and inequality measures such as Bonferroni and Lorenz curves. It also investigates the mean absolute deviation and entropy. Distributions of order statistics, reversed order statistics, and upper record values are also obtained. Additionally, univariate and bivariate moment structures are considered. The model parameters are estimated via the maximum likelihood method under simple random sampling and ranked set sampling, allowing an empirical evaluation of efficiency and reliability. Graphical representations exhibit the flexibility of the model, capturing various shapes in the probability density and hazard rate functions. To measure the practical quality of the model, actuarial metrics are used. A comparative analysis based on insurance, biomedical, and reliability datasets demonstrates the empirically improved performance and stability of the proposed new model for these specific datasets.

This paper delves into the theoretical and practical exploration of the complementary Bell Weibull (CBellW) model, which serves as an analogous counterpart to the complementary Poisson Weibull model. The study encompasses a comprehensive examination of various statistical properties of the CBellW model. Real data applications are carried out in three different fields, namely the medical, industrial and actuarial fields, to show the practical versatility of the CBellW model. For the medical data segment, the study utilizes four data sets, including information on daily confirmed COVID-19 cases and cancer data. Additionally, a Group Acceptance Sampling Plan (GASP) is designed by using the median as quality parameter. Furthermore, some actuarial risk measures for the CBellW model are obtained along with a numerical illustration of the Value at Risk and the Expected Shortfall. The research is substantiated by a comprehensive numerical analysis, model comparisons, and graphical illustrations that complement the theoretical foundation.

This paper introduces a novel continuous probability distribution on the unit interval called the unit Jamal distribution and explores its properties. The proposed distribution performs well in modeling bathtub-shaped data, effectively capturing its characteristic hazard rate behavior. Key mathematical characteristics such as moments, the moment generating function, order statistics, entropy, and the quantile function are thoroughly derived. Parameter estimation is conducted using maximum likelihood and Bayesian estimation methods. A simulation study is conducted to evaluate the accuracy of parameter estimates and to examine the distribution’s behavior. Additionally, the applicability of the proposed distribution is demonstrated through analysis of two real-world datasets, allowing for a comparison of its performance against existing models.

In this article, we introduce and investigate a new family of continuous distributions, termed the new Lomax-G (NLx-G) family, constructed via a novel generator. Several mathematical properties are derived, including quantile functions, mixture representations, and moments, together with different estimation methods. A notable special case, the NLx-exponential (NLxEx) distribution, is emphasized for its flexibility in modeling diverse data behaviors. The performance of the proposed model is examined through a comprehensive convergence analysis of estimators and supported by an extensive simulation study, which indicates that the maximum likelihood estimator performs best. To demonstrate practical utility, the NLxEx distribution is applied to three real-world datasets from hydrology, biomedical sciences, and insurance. In addition to standard goodness-of-fit measures, fitting plots are provided as further diagnostics. Across all applications and in comparison with several competing exponential-type models, the NLxEx distribution consistently yields the best fit, confirming its robustness and adaptability.