Model choice in separate families: A comparison between the FBST and the Cox test

ABSTRACT

The important problem of discriminating between separate families of distributions is the theme of this work. The Bayesian significance test, FBST, is compared with the celebrated Cox test. The three families most used in survival analysis, lognormal, gamma and Weibull, are considered for the discrimination. A convex combination—with unknown weights—of the three densities is used for this discrimination. After these weights have been estimated, the one with the highest value indicates the best statistical model among the three. Another important feature considered is the parameterization used. All the three densities are written as a function of the common population mean and variance. Including the weights, the number of parameters is reduced from eight (two of each density and two of the convex combination) to four (two from the common mean and variance plus two of the weights). Some numerical results from simulations are given. In these simulations, the results of FBST are compared with those obtained with the Cox test. Two real examples properly illustrate the procedures.

Keywords:

• Cox Test
• FBST
• Mixture model
• Model choice
• Separate Models
• Significance test

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F15
• 62F03

Acknowledgements

The authors are grateful to Mark Gannon for his support in technical and language editing, and proofreading of this manuscript, to referees and the editor for many perceptive comments and suggestions that improved the article. C.C. Assane and C. A. B. Pereira thank research fellowships from CNPq - Brazilian Research Funding Agency - processes 141349/2013-1 and 302767/2017-7, respectively.