Families of weighted distributions with inverse-hazard size bias: theory and applications

We studied a new class of weighted distributions in which the weighting mechanism introduces a size bias inversely proportional to the hazard rate of the baseline model. This formulation, referred to as the inverse-hazard size-biased distribution family, provided a flexible framework that unifies and extends several well-known two-parameter models. When one-parameter baseline distributions were considered, classical models such as the gamma, generalized Rayleigh, and beta prime distributions arise as particular cases of the proposed class. Furthermore, two new members based on the Maxwell and half-normal baseline distributions were introduced and studied in detail. Analytical properties, including moments and parameter estimation methods, were derived, and simulation studies were conducted to assess the performance of the estimators. The practical applicability of the proposed models was also illustrated through empirical analyses using real data.