Transformed Symmetric Models Gauss M. Cordeiro Departamento de Estat´ ıstica e Inform´atica, Universidade Federal Rural of Pernambuco, 52171-900, Recife, PE, Brazil e-mail: gauss@deinfo.ufrpe.br Marinho G. Andrade Departamento de Matematica Aplicada e Estat´ ıstica, Instituto de Ciˆ enciasMatem´aticasedeComputa¸c˜ao, Universidade de S˜ao Paulo, C.P.668, 13560-970, S˜ao Carlos, SP, Brazil e-mail: marinho@icmc.usp.br Abstract We introduce in this paper a new class of transformed symmetric models to ex- tend the Box and Cox (1964) models to more general symmetric models. This class of models includes all symmetric continuous distributions with a possible nonlinear structure for the mean and enables the fitting of a wide range of models to several data types. We derive an iterative process for fitting these models by maximum likelihood. We give simple formulae to estimate the parameter that index the trans- formation of the response variable and to estimate the rth moment of the original dependent variable which generalize previous published results. We discuss infer- ence on the parameters. The usefulness of the new class of models is illustrated in one application to a real data set. Key words: Box-Cox model, Dispersion parameter, Generalized linear model, Max- imum likelihood, Symmetric distribution, Transformation parameter. 1 Introduction We introduce a new class of transformed symmetric models (TSMs) with symmetric dis- tributions for the response variable and a possible nonlinear link function for the mean response. This class of models extend the classical Box and Cox (1964) models to cope with several other symmetric continuous distributions with heavier and lighter tails than the normal tails. We use a family of symmetric distributions to ensure that the ho- moscedasticity of the dispersion parameter holds since this is a common assumption in linear and nonlinear models. 1