  A common assumption regarding the standard tobit model is the normality of
the error distribution. However, asymmetry and bimodality may be present and
alternative tobit models must be used. In this paper, we propose a tobit model
based on the class of log-symmetric distributions, which includes as special
cases heavy and light tailed distributions and bimodal distributions. We
implement a likelihood-based approach for parameter estimation and derive a
type of residual. We then discuss the problem of performing testing inference
in the proposed class by using the likelihood ratio and gradient statistics,
which are particularly convenient for tobit models, as they do not require the
information matrix. A thorough Monte Carlo study is presented to evaluate the
performance of the maximum likelihood estimators and the likelihood ratio and
gradient tests. Finally, we illustrate the proposed methodology by using a
real-world data set.
