Mohammad A. Zayed

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.

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.

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.