This work proposes a new extension to the XLindley model called an inverse XLindley distribution (IXLD). Its probability density function and hazard rate function shapes were deduced mathematically. Several statistical properties of the IXLD were derived mathematically. We use ten different approaches to calculate the parameters of the IXLD. The asymptotic behaviour of these estimators were studied thanks to a comprehensive simulation investigation. Through modelling real data sets, the effectiveness and applicability of the IXLD are examined. This proves that the IXLD better fits the real data set than competing models.

The study describes the general concept of the XLindley distribution. Forms of density and hazard rate functions are investigated. Moreover, precise formulations for several numerical properties of distributions are derived. Extreme order statistics are established using stochastic ordering, the moment method, the maximum likelihood estimation, entropies and the limiting distribution. We demonstrate the new family’s adaptability by applying it to a variety of real-world datasets.

This article aims to introduce the inverse new XLindley distribution, a further extension of the new XLindley distribution. The article explores various properties of the proposed model, such as the quantile function, stochastic orders, entropies, fuzzy reliability, moments, and stress–strength estimation. The paper also compares different methods of estimating the parameters of the proposed model and evaluates their performance using a simulation study. Moreover, the paper demonstrates the usefulness of the proposed model by applying it to two real datasets. The article shows that the proposed model fits the data better than seven existing models based on model selection criteria, goodness-of-fit test statistics, and graphical visualizations. The paper concludes that the new model can be a valuable tool for modeling and analyzing hazard functions or survival data in various fields and contributing to probability theory and statistical inferences.

Animal Welfare has a significant impact on the dairy cow’s health, behaviour, productivity and milk quality. By implementing husbandry practices that respect the physical, behavioural and emotional needs of dairy cows, the dairy industry can improve the sustainability of its operations and meet rising expectations. The aim of this study is to evaluate the impact of housing systems (free vs. tied) on dairy cow health through musculoskeletal health indicators and lameness scores. The hypothesis that dairy cows reared in free housing have a better quality of health than cows reared in restrained housing is tested. Thus, 300 dairy cows of the Holstein and Montbeliarde breeds were selected from dairy farms in five municipalities of Constantine province (eastern Algeria). The results showed that the frequency of severe lameness did not exceed 12% in stalls with restraints and more than 42% of light lameness are in free-stall housing (p < 0.001). These results reflect a lack of comfort in restricted housing, with an impact on dairy performances. Moreover, the monitoring of lame cows and the functional trimming of their hooves should be frequent. It is also important to implement a cull policy for unproductive cows. Finally, it is very important to provide adequate training to farmers in order to improve the well-being of dairy cows.

In this paper, we investigate the dynamics of higher‐order solutions for a class of damped wave equations posed in R ⁿ and driven by a nonlocal cubic convolution source of Hartree type. The model incorporates a higher order Laplacian of order σ , spatially dependent density functions, and frictional damping mechanisms. Using energy methods combined with Hardy–Littlewood–Sobolev inequalities and higher order Sobolev embeddings, we establish the local well‐posedness of solutions in suitable high‐regularity spaces. We prove the global existence of solutions in the subcritical regime relative to the higher order Sobolev embedding and derive polynomial decay rates for the associated energy functional. The decay behavior is shown to depend explicitly on the order of the higher order operator and the singularity exponent of the convolution kernel.