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

Abstract

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.