On the one parameter unit-Lindley distribution and its associated regression model for proportion data

In this paper considering an appropriate transformation on the Lindley distribution, we propose the unit-Lindley distribution and investigate some of its statistical properties. An important fact associated with this new distribution is that it is possible to obtain the analytical expression for bias correction of the maximum likelihood estimator. Moreover, it belongs to the exponential family. This distribution allows us to incorporate covariates directly in the mean and consequently to quantify their influences on the average of the response variable. Finally, a practical application is presented to show that our model fits much better than the Beta regression.