Generalized Complementary Baseline Classes
Bibaseline; biometrics; applied statistics; probability.
This research aims to present two complementary generalized classes and bibaseline, denoted as Generalized Complementary Class Sine Bibaseline and Generalized Complementary Class Beta Bibaseline, respectively. These classes generalize and generate probability distributions through the composition of functions, enabling the discovery of new probabilistic distributions, classes of probabilistic distributions, and families of probability distributions. From this concept, expansions were developed for the cumulative distribution function and the probability density function. Identifiability studies were conducted for each, and properties characterizing the classes and their expansions were presented, including hazard function, moments and central moments of order m, moment generating function, characteristic function, and general coefficient. Additionally, derivatives of the log-likelihood function and support analysis were performed. Theoretical applications of the Class were demonstrated, followed by applications to simulated data and a real dataset, comparing the proposed model with existing models to assess its potential relative to others.