Growth estimates of cardinalfish (Epigonus crassicaudus) based on scale mixtures of skew-normal distributions

Our article presents a robust and flexible statistical model of the age–length relationship of cardinalfish (Epigonus crassicaudus). Specifically, we consider a non-linear regression model in which the error distribution allows for heteroskedasticity and belongs to the skew-normal (SMSN) distributions family of scale mixtures, thus eliminating the need to transform the dependent variable using techniques such as the Box–Cox transformation. The SMSN is a tractable and flexible class of asymmetric, heavy-tailed distributions that is useful for robust inference when the normality assumption for the error distribution is questionable. Two well-known important members of this class are the proper skew-normal and skew-t distributions. In this work, the skew-t model is emphasised. However, the proposed methodology can be adapted for each of the SMSN models with some basic changes. The present work is motivated by a previous analysis of cardinalfish where the oldest specimen was 15 years of age. In this study, we use the proposed methodology on a data set based on an otolith sample where the determined longevity is higher than 54 years.