A distribuição log-Bilal com zeros e/ou uns ajustados.

Abstract

When modeling data, it is common to work with variables limited to an interval. Although there are several distributions defined specifically to model these types of data, it is normal data such as proportions, rates and ratios contain zeros and/or ones and this makes it unfeasible to use a continuous distribution for modeling. Thus, in this dissertation, was proposed distributions built from the mixture between a log-Bilal distribution and a Bernoulli distribution degenerated in zero and/or one, in order to model data in the interval [0, 1], [0, 1) or (0, 1]. Monte Carlo simulations were also performed to study the properties of the maximum likelihood estimators. Finally, we present an illustration with a real data set.