A Neutrosophic Generalized Gamma Approach to Modeling PRL, LH, and Testosterone in Beagles

The Classical Generalized Gamma Distribution (GGD) has been widely applied in survival analysis, hydrology, and reliability engineering due to its flexibility in handling diverse data patterns. To incorporate uncertainty and imprecision commonly encountered in practical scenarios, this study introduces an extended form of the distribution, termed the Neutrosophic Generalized Gamma Distribution (NGGD). The NGGD is employed to investigate the secretion behavior of prolactin (PRL), luteinizing hormone (LH), and testosterone in male dogs. Analysis reveals that PRL exhibits a non-pulsatile, constitutive release pattern, which contrasts with the mixed pulsatile secretion observed in humans. The NGGD-based probability density functions further enable more accurate differentiation between control and drug-treated groups, aligning with established physiological evidence. These findings highlight the effectiveness of the NGGD in capturing biological variability under uncertainty, with potential applications extending to risk assessment, quality monitoring, and supply chain analysis.