The purpose of this paper is to look at how to estimate the finite population mean utilizing information from the auxiliary variable on a systematic sampling technique. By integrating the study variable’s maximum and minimum values, as well as two auxiliary variables, we offer estimators of the ratio, product, and regression types. The mathematical equations of the suggested and existing estimators are derived up to the first order of approximation. Based on real-life data sets, efficiency comparisons are carried out. The suggested ratio, product and regression estimators consistently outperform existing estimators in terms of mean square error, according to theoretical and empirical investigations.

This paper examines the vulnerability of Small and Medium-sized Enterprises (SMEs) exposed to evolving climate changes in Pakistan, specifically the impacts of extreme weather events, including floods and drought. The earlier literature illustrates that SMEs are affected by climate-related risks, but the current study takes the discussion further by implementing machine learning algorithms to measure the vulnerabilities of SMEs more objectively. A mixed-methods design was used to combine surveys with machine-learning techniques. PyCaret was employed to tune instruments such as Logistic Regression (LR), Random Forest (RF), ordered logistic regression, LightGBM, ADA Boost, SVM, KNN, GBC, and Naïve Bayes, among others, in Python. The results show that SMEs located in rural regions are significantly more vulnerable to climate events than SMEs in urban areas. The best results were found by the Logistic Regression model: its accuracy was 63.3%, recall 63.3%, F1-score 55.2%, and Kappa value 0.23. Random Forest showed similar findings, but Logistic Regression proved stronger in diagnosing the influence of climate on business activity. Ordered logistic regression-based analyses show that awareness of temperature fluctuation (p = 0.035) and perceived financial impact (p = 0.018) significantly affect the degree to which firms are affected by climate-related impacts, while geographic locations (p = 0.057) and business tenure (p = 0.091) are only marginally important. Strict evaluation of empirical evidence has pointed out that the application of focused financial tools, extensive infrastructure, and governance framework transformation can help to make the small- and medium-sized enterprises, especially enterprises located in remote areas to be more resilient to climate-related risks.. Further studies may improve this analysis through a more detailed machine-learning framework and analysis of sector-specific effects of climate change in specific geographic areas.

The Rayleigh flexible Weibull extension (RFWE) distribution, a new three-parameter model introduced in this paper, is a generalization of the flexible Weibull extension. This model produces best fit for failure time of electronic device obtained from power-linkage voltage spikes during electronic storms. We derive the statistical properties of the RFWE distribution. The parameters of this new distribution are estimated using the maximum likelihood method, which also yielded asymptotic confidence bounds. This model is examined using both real and simulated data. Under various priors, an additional Bayesian estimate is also carried out. The Bayes estimates and other posterior results are calculated using simulations.

High-dimensional gene expression datasets in chemometric and biomedical research present significant challenges for machine learning because the number of genes greatly exceeds the number of available samples, increasing the risk of overfitting and reducing classification reliability. Existing gene selection methods are often sensitive to noise and outliers, leading to unstable feature subsets and degraded classification performance. To address these limitations, this study proposes a Robust Masked Painter (RMP) framework that integrates robust measures of location and dispersion, namely the Median and the Rousseeuw & Croux statistic ($Q_n$), for reliable gene selection. The proposed framework operates in two stages. First, we identify informative genes using a round-robin strategy with a greedy search algorithm and robust core intervals to reduce the influence of noise and outliers. Second, Dominant Class (DC) analysis and Overlapping Scores (OS) further refine the selected gene subset by minimizing class overlap. We evaluate the proposed method on four publicly available gene expression datasets and compare it with several established feature selection methods using Random Forest, K-Nearest Neighbors, and Support Vector Machine classifiers. We assess classification performance using the Classification Error Rate. Experimental results and simulation studies demonstrate that the proposed RMP framework consistently outperforms competing methods by selecting highly informative genes that improve classification accuracy, robustness, and generalization.

In the current decade development of new distributions is a frequently used practice in probability theory. In this manuscript, we introduce a novel probability distribution which is referred as “Alpha Power Modified Inverse Rayleigh (APMIR) distribution”. Some important statistical properties of the suggested model have been derived and investigated thoroughly. These properties include higher order moments, Shannon and Renyi entropy, order statistics, mode etc. The maximum likelihood estimation (MLE) procedure is used to obtain estimates of the parameters of the suggested distribution. The performance of the proposed model is assessed using two real data sets. Simulation results are conducted to evaluate and justify the consistency of MLE. The suggested model offers better presentation as compared to other kinds of Rayleigh model.