Background: The cardiovascular crisis is advancing rapidly throughout the world. A large number of studies have shown that plant polyphenols affect major mechanisms involved in cardiovascular events through their action on the antioxidant system, signaling, and transcription pathways. D-limonene, a monocyclic monoterpene obtained from citrus fruits, is reported to possess many pharmacological activities. Methods: The experiment was designed to determine the protective effect of D-limonene against cardiac injury induced by CCl₄ in Wistar rats. Rats were treated with two doses of D-limonene against cardiac injury induced by CCl₄. Serum toxicity markers, cardiac toxicity biomarker enzymes, inflammatory mediators, anti-oxidant armory, lipid peroxidation, lipid profile, and histology were done. Results: CCl₄ intoxication resulted in a substantial rise in FFA, TC, TG, PL, LDL, VLDL, and a reduction in HDL, restoring these changes with the administration of D-limonene at a dosage of 200 mg/kg. CCl₄ administration also resulted in lipid oxidation and decreased antioxidant activity. At the same time, D-limonene at a dosage of 200 mg/kg body weight inhibited LPO and restored in vivo antioxidant components to normal. CC_l4 intoxication also resulted in a significant increase in inflammatory markers like IL-6, TNF-α, high sensitivity Corticotropin Releasing Factor (Hs-CRF), and biomarkers of cardiac toxicity like alanine aminotransferase (ALT), lactate dehydrogenase (LDH), creatine kinase (CK), creatine kinase MB (CKMB), and Troponin I & troponin-t activities. D-limonene reversed all these changes to normal. Histology further confirmed our obtained results. Conclusion: These findings indicate that D-limonene can ameliorate cardiac injury at a 200 mg/kg body weight dosage. Henceforth, D-Limonene intervenes in mediating CCl₄ induced toxicity by various signaling pathways. GRAPHICAL ABSTRACT

This study introduces a novel trigonometric-based family of distributions for modeling continuous data through a newly proposed framework known as the ASP family, where ‘ASP’ represents the initials of the authors Aadil, Shamshad, and Parvaiz. A specific subclass of this family, termed the “ASP Rayleigh distribution” (ASPRD), is introduced that features two parameters. We conducted a comprehensive statistical analysis of the ASPRD, exploring its key properties and demonstrating its superior adaptability. The model parameters are estimated using four classical estimation methods: maximum likelihood estimation (MLE), least squares estimation (LSE), weighted least squares estimation (WLSE), and maximum product of spaces estimation (MPSE). Extensive simulation studies confirm these estimation techniques’ robustness, showing that biases, mean squared errors, and root mean squared errors consistently decrease as sample sizes increase. To further validate its applicability, we employ ASPRD on three real-world engineering datasets, showcasing its effectiveness in modeling complex data structures. This work not only strengthens the theoretical framework of probability distributions but also provides valuable tools for practical applications, paving the way for future advancements in statistical modeling.

In this paper, a new generalization of Log Logistic Distribution using Alpha Power Transformation is proposed. The new distribution is named Alpha Power Log-Logistic Distribution. A comprehensive account of some of its statistical properties are derived. The maximum likelihood estimation procedure is used to estimate the parameters. The importance and utility of the proposed model are proved empirically using two real life data sets.

This study introduces a new and flexible class of probability distributions known as the novel alpha-power X (NAP-X) family. A key development within this framework is the novel alpha-power half-logistic (NAP-HL) distribution, which extends the classical half-logistic model through an alpha-power transformation, allowing for greater adaptability to various data shapes. The paper explores several theoretical aspects of the proposed model, including its moments, quantile function and hazard rate. To assess the effectiveness of parameter estimation, a detailed simulation study is conducted using seven estimation techniques: Maximum likelihood estimation (MLE), Cramér–von Mises estimation (CVME), maximum product of spacings estimation (MPSE), least squares estimation (LSE), weighted least squares estimation (WLSE), Anderson–Darling estimation (ADE) and a right-tailed version of Anderson–Darling estimation (RTADE). The results offer comparative insights into the performance of each method across different sample sizes. The practical value of the NAP-HL distribution is demonstrated using two real datasets from the metrology and engineering domains. In both cases, the proposed model provides a better fit than the traditional half-logistic and related distributions, as shown by lower values of standard model selection criteria. Graphical tools such as fitted density curves, Q–Q and P–P plots, survival functions and box plots further support the suitability of the model for real-world data analysis.