We introduce the heavy-tailed Weibull flexible-G (HT-WF-G) family of distributions and derive its fundamental properties, including quantile functions and moments. A maximum likelihood estimation procedure is developed for the parameter inference, with its finite-sample performance and asymptotic properties validated through rigorous Monte Carlo simulation studies. Furthermore, we formulate key actuarial risk metrics including the value at risk (VaR), tail value at risk (TVaR), tail variance (TV), and tail variance premium (TVP) within this flexible framework. The model's practical effectiveness is demonstrated through its application to oncology time-to-event data (lung cancer and acute myeloid leukemia). Empirical results consistently affirm the model's superiority over leading benchmark distributions, as evidenced by significant improvements in the goodness-of-fit criteria, thus establishing the HT-WF-G family as an effective tool for statistical modeling in heavy-tailed and complex survival settings.

In this article, Autism Spectrum Disorder (ASD) is discussed, with an emphasis placed on the multidimensional nature of the disorder, which is anchored in genetic and neurological components. Identifying genes related to ASD is essential to comprehend the mechanisms that underlie the illness, yet the condition's complexity has impeded precise information in this field. In ASD research, the analysis of gene expression data helps choose and categorize significant genes. The study used microarray data to provide a novel approach that integrated gene selection techniques with deep learning models to improve the accuracy of ASD prediction. It offered a detailed comparative examination of gene selection approaches and deep learning architectures, including singular value decompositions (SVD), principal component analyses (PCA), and convolutional neural networks (CNNs). This paper combines gene selection methods (PCA and SVD) with deep learning models (CNN) to improve ASD prediction. Compared to more traditional approaches, the study revealed that its integrated methodology was more effective in improving the accuracy of ASD prediction results through experimentation. There was a difference in the accuracy between the PCA-CNN model, which achieved 94.33% with a loss of 0.4312, and the SVD-CNN model, which achieved 92.21% with a loss less than or equal to 0.3354. These discoveries help in the development of more accurate diagnostic and prognostic tools for ASD, which is a complicated neurodevelopmental disorder. Additionally, they provide insights into the molecular pathways that underlie ASD.