A discrete extension of the Lindley distribution for health and sustainability data: Theoretical insights and decision-making applications

Integrating SDG 3 (Good Health and Well-Being) with an innovative discrete probability model for lifetime data provides a comprehensive approach to achieving sustainable health outcomes and analyzing lifetime data within sustainability frameworks. This model captures the discrete nature of lifetime measurements frequently found in patient records, equipment longevity, and treatment interval by drawing on the Kumaraswamy family for accuracy. Its essential statistical features, including hazard rate, moments, dispersion index, skewness, and entropy, support robust health data analysis, enhancing SDG 3 by improving our understanding of survival trends in patients and medical devices. Additionally, the model's adaptability to asymmetric dispersion across various kurtosis types (mesokurtic, platykurtic, and leptokurtic) allows it to address variability in health outcomes influenced by demographic or treatment factors. The flexible hazard rate function spanning decreasing, bathtub-shaped, and constant rates makes it well-suited for a range of health applications, from chronic disease management to mortality studies. Furthermore, its capacity to handle zero-inflated and over- or under-dispersed data, commonly seen in health research, enables a more refined public health analysis crucial for SDG 3. With maximum likelihood estimation for parameter fitting, the model has been validated in practical sustainability contexts, such as monitoring patient follow-ups, evaluating device reliability, and examining disease progression, offering valuable insights for sustainable health interventions and effective resource use.