The power XLindley (PXL) distribution is introduced in this study. It is a two-parameter distribution that extends the XLindley distribution established in this paper. Numerous statistical characteristics of the suggested model were determined analytically. The proposed model’s fuzzy dependability was statistically assessed. Numerous estimation techniques have been devised for the purpose of estimating the proposed model parameters. The behaviour of these factors was examined using randomly generated data and developed estimation approaches. The suggested model seems to be superior to its base model and other well-known and related models when applied to the COVID-19 data set.

We conducted surveys of Mediterranean beaches in Egypt, Morocco, and Tunisia including 37 macro-litter (> 25 mm) and 41 meso-litter (5–25 mm) assessments. Our study identified key litter items and assessed pollution sources on urban, semi-urban, tourist, and semi-rural beaches. Macro-litter concentration averaged 5032 ± 4919 pieces per 100 m or 1.71 ± 2.28 pieces/m², with higher values observed on urban (mean 2.63 pieces/m² ± 3.03) and tourist (mean 1.23 pieces/m² ± 0.91) beaches. Similarly, urban (mean 9.91 pieces/m² ± 12.70) and tourist beaches (mean 5.32 pieces/m² ± 4.48) revealed elevated levels of meso-litter contamination, particularly in the upper third of the beach, which contained the highest quantities both in terms of number (51%) and weight (50%). 55% of the macro-litter and 35% of the meso-litter originated from human shoreline activities and poor waste management. Given the width of some beaches and their high levels of pollution, the standard 100 m macro-litter approach was impractical. To enable cost-effective, long-term monitoring, we adapted it to a faster 10 m transect approach, which provided reliable data on the top 25 litter items, accounting for 82% of beach pollution. Our Sand Rake method effectively quantified pollution on both cleaned and uncleaned beaches, addressing the often neglected meso-litter size fraction. The high pollution levels, top litter items, and identified sources indicate that beach cleaning alone will not solve the pollution problem. Efforts to raise environmental awareness, enhanced waste management, and law enforcement are needed to improve the situation in a sustainable way.

In this paper, we emphasize a new one-parameter distribution with support as $[1,+\infty )$. It is constructed from the inverse method applied to an understudied one-parameter unit distribution, the unit Teissier distribution. Some properties are investigated, such as the mode, quantiles, stochastic dominance, heavy-tailed nature, moments, etc. Among the strengths of the distribution are the following: (i) the closed-form expressions and flexibility of the main functions, and in particular, the probability density function is unimodal and the hazard rate function is increasing or unimodal; (ii) the manageability of the moments; and, more importantly, (iii) it provides a real alternative to the famous Pareto distribution, also with support as $[1,+\infty )$. Indeed, the proposed distribution has different functionalities but also benefits from the heavy-right-tailed nature, which is demanded in many applied fields (finance, the actuarial field, quality control, medicine, etc.). Furthermore, it can be used quite efficiently in a statistical setting. To support this claim, the maximum likelihood, Anderson–Darling, right-tailed Anderson–Darling, left-tailed Anderson–Darling, Cramér–Von Mises, least squares, weighted least-squares, maximum product of spacing, minimum spacing absolute distance, and minimum spacing absolute-log distance estimation methods are examined to estimate the unknown unique parameter. A Monte Carlo simulation is used to compare the performance of the obtained estimates. Additionally, the Bayesian estimation method using an informative gamma prior distribution under the squared error loss function is discussed. Data on the COVID mortality rate and the timing of pain relief after receiving an analgesic are considered to illustrate the applicability of the proposed distribution. Favorable results are highlighted, supporting the importance of the findings.

The extended reduced Kies distribution (ExRKD), which is an asymmetric flexible extension of the reduced Kies distribution, is the subject of this research. Some of its most basic mathematical properties are deduced from its formal definitions. We computed the ExRKD parameters using eight well‐known methods. A full simulation analysis was done that allows the study of these estimators’ asymptotic behavior. The efficiency and applicability of the ExRKD are investigated via the modeling of COVID‐19 and milk data sets, which demonstrates that the ExRKD delivers a better match to the data sets when compared to competing models.

Modifying the existing probability models in the literature and introducing new extensions of the existing probability models is a prominent and interesting research topic. However, in the most recent era, the extensions of the probability models via trigonometry methods have received great attention. This paper also offers a novel trigonometric version of the Weibull model called a new alpha power cosine-Weibull (for short, “NACos-Weibull”) distribution. The NACos-Weibull distribution is introduced by incorporating the cosine function. Certain distributional properties of the NACos-Weibull model are derived. The estimators of the NACos-Weibull model are derived by implementing the maximum likelihood approach. Three simulation studies are provided for different values of the parameters of the NACos-Weibull distribution. Finally, to demonstrate the effectiveness of the NACos-Weibull model, three applications from the hydrological and engineering sectors are considered.

In the field of life testing, it is very important to study the reliability of any component under testing. One of the most important subjects is the “stress‐strength reliability” term which always refers to the quantity P (X > Y) in any statistical literature. It resamples a system with random strength (X) that is subjected to a random strength (Y) such that a system fails in case the stress exceeds the strength. In this study, we consider stress‐strength reliability where the strength (X) follows Rayleigh‐half‐normal distribution and stress (Y₁, Y₂, Y₃, and Y₄) follows Rayleigh‐half‐normal distribution, exponential distribution, Rayleigh distribution, and half‐normal distribution, respectively. This effort comprises determining the general formulations of the reliabilities of a system. Also, the maximum likelihood estimation approach and method of moment (MOM) will be utilized to estimate the parameters. Finally, reliability has been attained utilizing various values of stress and strength parameters.