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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.

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 ( Y 1 , Y 2 , Y 3 , and Y 4 ) 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.

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Wasting is one of the symptoms of malnutrition that has been connected to the deaths of malnourished children. This study was intended to explain the effect of socio‐demographic and economic factors on under‐5 wasting by evaluating their conditional effect across the distribution of weight‐for‐height Z (WHZ) scores using the quantile regression (QR) model. The weighted sample which included 13,680 children under 5 years was taken from the countrywide Egyptian DHS 2014 survey. The results depicted that about 2% of Egyptian children were severely wasted, with the prevalence of wasting being around 8%. It was discovered that across the WHZ distribution, the child's features, maternal characteristics, father's education, and social factors had significant but varied contributions in explaining the wasting status of under‐5 children. It was revealed that female children had a significant weight advantage, notably 0.21 standard deviation (SD) higher weight at the 95th quantile over their male counterparts. The WHZ score was also found to be significantly positively associated with both age and household's wealth status at the lower and upper tails of the WHZ distribution, respectively. Moreover, in comparison with children whose mothers were underweight, those whose mothers were normal or overweight had higher WHZ scores, with a 1.45 SD increase in WHZ scores at the 95th quantile for mothers who were normal weights. Furthermore, the children who were breastfed, whose mothers received antenatal care (ANC) services, and/or who had educated parents had an advantage in terms of WHZ scores than their counterparts. In addition, the children with higher birth order and/or who resided in urban areas had weight disadvantages compared to their counterparts. Therefore, in order to improve children's nutritional status and achieve the Sustainable Development Goals (SDGs) by 2030, the government and public–private owner organizations must work together at the community level focusing on vulnerable groups.