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In this work we show a Bayesian quantile regression method to responsevariables with mixed discrete-continuous distribution with a point mass atzero, where these observations are believed to be left censored or true zeros.We combine the information provided by the quantile regression analysis topresent a more complete description of the probability of being censored giventhat the observed value is equal to zero, while also studying the conditionalquantiles of the continuous part. We build up an Markov Chain Monte Carlomethod from related models in the literature to obtain samples from theposterior distribution. We demonstrate the suitability of the model to analyzethis censoring probability with a simulated example and two applications withreal data. The first is a well known dataset from the econometrics literatureabout women labor in Britain and the second considers the statistical analysisof expenditures with durable goods, considering information from Brazil.

Bayesian quantile regression analysis for continuous data with a discrete component at zero