Statistical Modelling 13 (2) (2013), 125–151
A regression model for special proportions
Gustavo HA Pereira
Department of Statistics,
University of São Paulo,
Brazil
e-mail: ghapereira@terra.com.br
Denise A Botter
Insper Institute of Education and Research,
Brazil
Mônica C Sandoval
Insper Institute of Education and Research,
Brazil
Abstract:
Credit cards are a financial product with special characteristics. Dividing the amount paid by the customer in a given month by the total bill results in a variable that is partly discrete and partly continuous, which we call the relative payment amount (RPA). This variable is discrete at 0, c and 1, and it is continuous in the open interval (c, 1). The 0 < c <1 value is known and is given by the ratio between the value of the minimum payment and the full amount, and this value is not fixed for all customers. Thus, in practice, the RPA is a variable whose support of its distribution is non-constant across population units. In this work, we propose a regression model for the RPA. The model allows all of the unknown parameters of the conditional distribution of the response variable to be modelled as a function of the explanatory variables, and it also accounts for the non-constant known parameter c. The estimation of the parameters of this model is discussed, diagnostic analysis is addressed and closed-form expressions for the score function and for the Fisher’s information matrix are provided. Moreover, some results related to the non-constant nature of c are obtained, simulation studies are performed and an application using real credit card data is presented.
Keywords:
beta distribution; credit card; inflated distributions; maximum likelihood estimator; proportions; truncated beta distribution
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