The paper first introduces a new two-parameter continuous probability distribution
with bounded support from the extended exponential-geometric distribution. Closed-
form expressions are given for the moments, moments of the order statistics and
quantile function of the new law; it is also shown that the members of this family of
distributions can be ordered in terms of the likelihood ratio order. The parameter
estimation is carried out by the method of maximum likelihood and a closed-form
expression is given for the Fisher information matrix, which is helpful for asymptotic
inferences. Then, a new regression model is introduced by considering the proposed
distribution, which is adequate for situations where the response variable is restricted
to a bounded interval, as an alternative to the well-known beta regression model,
among others. It relates the median response to a linear predictor through a link
function. Extensions for other quantiles can be similarly performed. The suitability
of this regression model is exemplified by means of a real data application.