  In this work we show a Bayesian quantile regression method to response
variables with mixed discrete-continuous distribution with a point mass at
zero, where these observations are believed to be left censored or true zeros.
We combine the information provided by the quantile regression analysis to
present a more complete description of the probability of being censored given
that the observed value is equal to zero, while also studying the conditional
quantiles of the continuous part. We build up an Markov Chain Monte Carlo
method from related models in the literature to obtain samples from the
posterior distribution. We demonstrate the suitability of the model to analyze
this censoring probability with a simulated example and two applications with
real data. The first is a well known dataset from the econometrics literature
about women labor in Britain and the second considers the statistical analysis
of expenditures with durable goods, considering information from Brazil.
