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

Abstract 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.

[1]  A. Punt,et al.  Modelling growth of rock lobsters, Jasus edwardsii, off Victoria, Australia using models that allow for individual variation in growth parameters , 2006 .

[2]  Yat Sun Poon,et al.  Conformal normal curvature and assessment of local influence , 1999 .

[3]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[4]  H. Chai,et al.  Use of log‐skew‐normal distribution in analysis of continuous data with a discrete component at zero , 2008, Statistics in medicine.

[5]  A. Azzalini,et al.  Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t‐distribution , 2003, 0911.2342.

[6]  D. Rubin,et al.  The ECME algorithm: A simple extension of EM and ECM with faster monotone convergence , 1994 .

[7]  D K Kimura,et al.  Testing nonlinear regression parameters under heteroscedastic, normally distributed errors. , 1990, Biometrics.

[8]  Rodrigo Wiff,et al.  La longevidad del besugo Epigonus crassicaudus en Chile: ¿es similar a la de sus parientes? , 2010 .

[9]  Sik-Yum Lee,et al.  Local influence for incomplete data models , 2001 .

[10]  André E. Punt,et al.  Admitting ageing error when fitting growth curves: an example using the von Bertalanffy growth function with random effects , 2007 .

[11]  Jianxin Pan,et al.  Growth curve models and statistical diagnostics , 2002 .

[12]  K. R. Allen.  A Method of Fitting Growth Curves of the von Bertalanffy Type to Observed Data , 1966 .

[13]  Liang Xu,et al.  Influence analyses of nonlinear mixed-effects models , 2004, Comput. Stat. Data Anal..

[14]  Russell B. Millar.  Reference priors for Bayesian fisheries models , 2002 .

[15]  L. Walford,et al.  Bioenergetics and Growth , 1947 .

[16]  Javier E. Contreras-Reyes,et al.  Shannon Entropy and Mutual Information for Multivariate Skew‐Elliptical Distributions , 2013 .

[17]  K. Lange,et al.  Normal/Independent Distributions and Their Applications in Robust Regression , 1993 .

[18]  Marc G. Genton,et al.  Skew-elliptical distributions and their applications : a journey beyond normality , 2004 .

[19]  S. Candy,et al.  A VON BERTALANFFY GROWTH MODEL FOR TOOTHFISH AT HEARD ISLAND FITTED TO LENGTH-AT-AGE DATA AND COMPARED TO OBSERVED GROWTH FROM MARK-RECAPTURE STUDIES , 2007 .

[20]  Estimation and diagnostics for heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions , 2012 .

[21]  H. Akaike.  A new look at the statistical model identification , 1974 .

[22]  D. Kimura.  LIKELIHOOD METHODS FOR THE VON BERT ALANFFY GROWTH CURVE , 1980 .

[23]  J. Quiroz,et al.  Estado de explotación del recurso besugo (Epigonus crassicaudus) en Chile , 2005 .

[24]  Victor H. Lachos,et al.  Robust mixture modeling based on scale mixtures of skew-normal distributions , 2010, Comput. Stat. Data Anal..

[25]  T. Beard,et al.  Age-validated Longevity of Fishes: Its Importance for Sustainable Fisheries , 2008 .

[26]  Luis A. Cubillos,et al.  Verificación de la edad y crecimiento de besugo Epigonus crassicaudus (de Buen, 1959) admitiendo error en la determinación de la edad , 2009 .

[27]  R Core Team,et al.  R: A language and environment for statistical computing. , 2014 .

[28]  D. Dey,et al.  A General Class of Multivariate Skew-Elliptical Distributions , 2001 .

[29]  Heteroscedastic nonlinear regression models based on scale mixtures of skew-normal distributions. , 2011 .

[30]  R. Arellano-Valle,et al.  LIKELIHOOD BASED INFERENCE FOR SKEW-NORMAL INDEPENDENT LINEAR MIXED MODELS , 2010 .

[31]  John M. Hoenig,et al.  Comparison of two approaches for estimating natural mortality based on longevity , 2005 .