Growth curve based on scale mixtures of skew-normal distributions to model the age-length relationship of Cardinalfish (Epigonus Crassicaudus)

摘要

Our article presents a robust and flexible statistical modeling for thegrowth curve associated to the age-length relationship of Cardinalfish(Epigonus Crassicaudus). Specifically, we consider a non-linear regressionmodel, in which the error distribution allows heteroscedasticity and belongs tothe family of scale mixture of the skewnormal (SMSN) distributions, thuseliminating the need to transform the dependent variable into many data sets.The SMSN is a tractable and flexible class of asymmetric heavy-taileddistributions that are useful for robust inference when the normalityassumption for error distribution is questionable. Two well-known importantmembers of this class are the proper skew-normal and skew-t distributions. Inthis work emphasis is given to the skew-t model. However, the proposedmethodology 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 thisstudy we carry out the mentioned methodology over a data set that include along-range of ages based on an otolith sample where the determined longevity ishigher than 54 years.