This study presents a new two-parameter lifetime model, the exponentiated modified Lindley distribution, which extends the flexibility of the traditional modified Lindley distribution. The proposed model was constructed using an exponentiation approach that introduces an additional shape parameter, allowing it to accommodate a wide variety of data patterns and hazard rate behaviors. Comprehensive analytical properties were investigated, including moments and reliability characteristics, along with several parameter estimation methods. In addition to classical estimation techniques, a Bayesian estimation procedure was developed for the exponentiated modified Lindley distribution, as well as a bootstrap approach for constructing confidence intervals for the model parameters. A simulation study was conducted to assess the efficiency and robustness of the proposed estimators. Furthermore, applications to real datasets demonstrated that the proposed model provides an improved fit compared to conventional lifetime distributions. These results indicate that the exponentiated modified Lindley distribution is a valuable addition to the class of continuous distributions, offering enhanced adaptability for modeling reliability, survival, and other forms of asymmetric data encountered in applied statistics.

Early and accurate diagnosis of lung cancer remains challenging due to the heterogeneity of tumor morphology and the variability across imaging modalities. This study proposed a deep learning framework that integrated computed tomography (CT), positron emission tomography/computed tomography (PET/CT), and chest X-ray (CXR) within a unified multi-modal transformer architecture for early lung cancer detection. The framework employed modality-specific encoders combining convolutional and state-space blocks to extract spatial-frequency representations, followed by a gated cross-modal fusion transformer designed to align heterogeneous features and handle missing modalities through mixture-of-experts routing and low-rank imputation. Multi-task heads were jointly optimized for nodule detection, segmentation, malignancy classification, and survival risk prediction. Explainability was embedded through concept bottlenecks, prototype reasoning, gradient-based attribution, and counterfactual concept editing, offering case-level interpretability and clinically meaningful evidence maps. Uncertainty was estimated via Monte-Carlo dropout, deep ensembles, and temperature scaling to ensure calibrated confidence estimates and defer-to-expert safety decisions. Lung image database consortium and image database resource initiative (LIDC-IDRI) (CT), the cancer imaging archive (TCIA) (PET/CT), and national lung screening trial (NLST) (CXR) benchmark datasets revealed that our methods work better than the best methods available. The proposed technique yielded Dice scores of 0.879, 0.872, and 0.876, together with AUC values of 0.944, 0.952, and 0.938, and an expected calibration error (ECE) of 0.02 across all modalities. Under domain shift, cross-dataset analysis showed substantial generalization ( $AUC>0.92$). A generalizable framework for multi-modal diagnostics made it possible to use AI to help with lung cancer screening in a way that was clear, trustworthy, and scalable.

Multicollinearity presents a significant challenge in zero-inflated negative binomial (ZINB) regression, leading to unstable maximum likelihood estimates (MLEs) and inflated prediction errors. To address this issue, we investigated the performance of the Kibria-Lukman estimator (ZINB-KLE) and proposed a modified Kibria-Lukman estimator (ZINB-MKLE) that introduces an enhanced bias-adjustment mechanism for improved coefficient stability. Using extensive Monte Carlo simulations under varying degrees of multicollinearity and overdispersion, we demonstrated that the ZINB-MKLE consistently achieves substantially lower scalar mean squared error (SMSE) than MLEs, ZINB-KLEs, and other competing estimators. Application to the Blood Transfusion dataset further confirmed the practical advantages of the ZINB-MKLE, yielding an SMSE of 1.8568 compared to 14,638.75 for the MLE and 685.81 for the ZINB-KLE, highlighting dramatic improvements in predictive accuracy. These findings establish the ZINB-MKLE as a robust and efficient alternative for handling multicollinearity in zero-inflated regression models, with broad implications for statistical modeling in biomedical, epidemiological, and other applied data settings.