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

TL;DR

This paper introduces a flexible statistical growth curve model using scale mixtures of skew-normal distributions to accurately describe the age-length relationship of Cardinalfish, accommodating heteroscedasticity and heavy tails.

Contribution

It develops a robust non-linear regression approach with SMSN error distributions, especially skew-t, for modeling fish growth without data transformation.

Findings

Model effectively captures asymmetric heavy-tailed data.

Method applied to Cardinalfish with ages up to 54 years.

Provides a flexible framework for growth curve analysis.

Abstract

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.