  In statistical modeling area, the Akaike information criterion AIC, is a
widely known and extensively used tool for model choice. The {\phi}-divergence
test statistic is a recently developed tool for statistical model selection.
The popularity of the divergence criterion is however tempered by their known
lack of robustness in small sample. In this paper the penalized minimum
Hellinger distance type statistics are considered and some properties are
established. The limit laws of the estimates and test statistics are given
under both the null and the alternative hypotheses, and approximations of the
power functions are deduced. A model selection criterion relative to these
divergence measures are developed for parametric inference. Our interest is in
the problem to testing for choosing between two models using some informational
type statistics, when independent sample are drawn from a discrete population.
Here, we discuss the asymptotic properties and the performance of new procedure
tests and investigate their small sample behavior.
