Background: Green extraction involves using green solvents, such as water, to reduce energy consumption, avoid health and environmental hazards and induce the quality and quantity of the extract. Date palm fruits are a vital source of food and medicinal activities, as they contain a high diversity of phytochemicals, mainly phenolic and flavonoid compounds. The main aim of this study is to investigate the use of water as a green solvent, when assisted by different ultrasonic frequencies, in the extraction of four different cultivars of date palm fruits, by evaluating the phenolic and flavonoid composition as well as the antioxidant capacity of the extract. Methods: Four date palm fruits’ cultivars (Agwa, Anbarah, Khalas, and Reziz) were extracted using conventional methods (by water and ethanol) and by ultrasonic means, using two frequencies, 28 and 40 kHz, and applying temperatures (30, 45, and 60 °C), also measuring extraction times (20, 40, 60 min.). Response surface methodology was used for the statistical analysis, applying three factors (temperature, time, and ultrasonic frequency), four responses (total phenolic content, total flavonoid content, FRAP, and ABTS), and four cultivars (categories). Results: Conventional water extraction obtained minimal phenolic and flavonoid compounds (up to 52% of ethanol extraction). This percent improved to reach 60% when heat was utilized. The application of ultrasonic frequencies significantly enhanced the extraction of phenolics/flavonoids and the antioxidant ability of the extract to nearly 90% and 80%, respectively. The use of 40 kHz ultrasonic power managed to extract more phenolic and flavonoid components; however, the antioxidant capacities of the extract were less than when the 28 kHz power was utilized. Agwa and Khalas demonstrated themselves to be the best cultivars for ultrasonic-assisted extraction, depending on the results of the optimized responses. Conclusion: This study could be implemented in the industry to produce date palm fruits’ enriched extracts with phenolic and flavonoid components and/or antioxidants.

One of the challenges, when investigating sensitive attributes, or information that people tend not to disclose, through surveys is the ethical obligation to preserve the privacy of respondents. Although the randomized response method, originally suggested by Warner, allows estimating the proportion of such attributes within the population while maintaining confidentiality, the variance of the estimate consistently increases if the likelihood of selecting the question about sensitive attribute increases. The purpose of this research is to introduce a new three-stage RR model which provides an efficient alternative to Warner's model that allows more credibility from a practical perspective and apply the model to estimate noncompliance ratio in compulsory motor insurance. For the two models, a measure of privacy protection was calculated and a relation between this measure and the efficiency of both models was introduced. Efficiency comparisons indicate that the proposed model can always be made more efficient than both Warner's and Mangat & Singh's RR models. The proposed model, with specific parameter selection, was applied on a selected population and proved a practical reliability. The noncompliance ratio to obtain compulsory motor insurance was estimated by both a point and a confidence interval. This estimate provides a basis to predict third party motor insurance inclusion.

The current research offers an enhanced three-parameter lifetime model that combines the unit Burr XII distribution with a power series distribution. The novel class of distribution is named the unit Burr XII power series (UBXIIPS). This compounding technique allows for the production of flexible distributions with strong physical meanings in domains such as biology and engineering. The UBXIIPS class includes the unit Burr XII Poisson (UBXIIP) distribution, the unit Burr XII binomial distribution, the unit Burr XII geometric distribution, and the unit Burr XII negative binomial distribution. The statistical properties of the class include formulas for the density and cumulative distribution functions, and limiting behaviour, moments and incomplete moments, entropy measures, and quantile function are provided. For estimating population parameters and fuzzy reliability for the UBXIIP model, maximum likelihood and Bayesian approaches are studied by the Metropolis–Hastings algorithm. For maximum likelihood estimators, the length of asymptotic confidence intervals is specified, whereas, for Bayesian estimators, the length of credible confidence intervals is assigned. A simulation investigation of the UBXIIP model was established to evaluate the performance of suggested estimates. In addition, the UBXIIP distribution is explored using real-world data. The UBXIIP distribution appears to offer some benefits in understanding lifetime data when compared to unit Weibull, beta, Kumaraswamy, Kumaraswamy Kumaraswamy, Marshall-Olkin Kumaraswamy, and Topp–Leone Weibull Lomax distributions.

The existence of potential incomplete truthful reporting emerges when dealing with topics of great sensitivity. This paper introduces a novel, efficient randomized response model to address the challenges of untruthful reporting. It is meant to improve the accuracy of estimating highly sensitive attributes. The suggested model represents a modified version of Aboalkhair's model (2024) that was found to be an efficient substitute for the models developed by Warner and Mangat & Singh. This study examines the circumstances under which the suggested model outperforms alternative models in terms of efficiency. Theoretical and numerical comparisons of efficiency with alternative models, assuming incomplete truthful reporting, revealed the superior performance of the suggested model. Furthermore, a measure of privacy protection is computed.

This paper suggests an innovative randomized response model utilizing customizable random tool. The suggested model offers a general framework for some previously pioneering randomized response models and generates new efficient models. Comparison of the efficiency between one of these newly generated models and other groundbreaking models through theoretical and numerical ways, demonstrates higher efficiency for the new generated model. Additionally, ethical considerations and privacy protection of the suggested model are examined.