Inflated Unit Gamma Distribution
Inflated data; unit gamma distribution; inflated unit gamma distribution.
A unit range distribution model may contain variables in the range (0,1), however, in some scenarios, or data set the values zeros and/or ones. In this case, the modeling is directed to variables that assume values in the intervals (0,1], [0,1) or [0,1], and as such, it is necessary to analyze such data sets using appropriate inflated models. In this article we propose the inflated unit gamma distribution and present its main properties. We derive expressions for the maximum likelihood estimators from the distribution parameters and perform a Monte Carlo simulation study to evaluate such estimators. In addition, simulations are also conducted to evaluate the behavior of the asymptotic confidence interval and hypothesis tests, in small samples. Additionally, two applications were made to real data to illustrate the usefulness of the proposed distribution.