Note on the family of proportional reversed hazard distributions

For many years, authors have been interested in developing methods for generating distributions that provide a flexible family to model lifetime variables. This paper proposes an exact inference approach to the family of proportional reversed hazard distributions based on the pivotal quantity, which yields exact confidence intervals with the shortest-length as well as reasonable estimators for the family of proportional reversed hazard distributions. In addition, the approach is extended to functions related to the unknown parameters using a generalized pivotal quantity such as the the goodness of fit test and entropy issues without computational complexity. The proposed method is illustrated through Monte Carlo simulations and real data analysis.