Browsing by Author "HAMAMI, Loubna"

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    Estimation in frailty models
    (Université Badji Mokhtar Annaba, 2025) HAMAMI, Loubna
    Fragility models are essential for survival data as they address the issue of unobserved heterogeneity, which can arise from various factors such as genetic predisposition, environmental influences, or lifestyle choices. In this study, we propose two new fragility models: the quasi Xgamma model (QXg-F) and the Mixed Gamma-Exponential model (MGEF) to account for this unobserved heterogeneity in univariate survival data. Fragility is incorporated multiplicatively into the baseline hazard function. We derive the unconditional survival and hazard functions using the Laplace transform of the fragility distribution, considering Weibull and compertz hazard functions as bases, and we estimate the parameters using the maximum likelihood method. We employ the Nikulin-Rao-Robson goodness-of-fit test to assess model adequacy. Through simulation studies, we demonstrate how the QXg-F and MGEF models capture heterogeneity and enhance model fit, evaluating their performance under various right censoring rates and testing the likelihood ratio’s ability to detect unobserved heterogene- ity based on sample size. We also apply these models to real data, including a new dataset collected from an emergency hospital in Algeria. Our findings suggest that the QXg-F and MGEF models are viable alternatives to existing fragility modeling distributions and have the potential to improve the accuracy of survival analyses across various fields, in-cluding emergency care. Additionally, we examine the effectiveness and relevance of the QXg-F model in the insurance sector through simulations and applications to insurance data.