  Our article presents a robust and flexible statistical modeling for the
growth curve associated to the age-length relationship of Cardinalfish
(Epigonus Crassicaudus). Specifically, we consider a non-linear regression
model, in which the error distribution allows heteroscedasticity and belongs to
the family of scale mixture of the skewnormal (SMSN) distributions, thus
eliminating the need to transform the dependent variable into many data sets.
The SMSN is a tractable and flexible class of asymmetric heavy-tailed
distributions that are useful for robust inference when the normality
assumption for error distribution is questionable. Two well-known important
members of this class are the proper skew-normal and skew-t distributions. In
this work emphasis is given to the skew-t model. However, the proposed
methodology can be adapted for each of the SMSN models with some basic changes.
The present work is motivated by previous analysis about of Cardinalfish age,
in which a maximum age of 15 years has been determined. Therefore, in this
study we carry out the mentioned methodology over a data set that include a
long-range of ages based on an otolith sample where the determined longevity is
higher than 54 years.
