Goodness-of-fit test of normality against GEP alternatives

Alain Desgagné (1) , Pierre Lafaye de Micheaux (2, 3) , Alexandre Leblanc (4)

1 DMS - Département de Mathématiques et de statistique [UdeM- Montréal]
2 SAGAG - Statistique Appliquée et de Géométrie Aléatoire de Grenoble
3 GIN - Grenoble Institut des Neurosciences
4 Department of Statistics

The generalized exponential power (GEP) density has a large range of tails behavior, which may be exponential, polynomial or logarithmic. Taking this family of densities as an alternative, a normality test based on Rao's score test statistic is proposed. Since the normal density is a special case of the GEP density, this is equivalent to testing a simple null hypothesis about the GEP density parameters. The main interest in this approach is to provide a powerful test against alternatives with non-normal tails. A Monte Carlo simulation study is performed to evaluate the level and power of the test.

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Alain Desgagné, Pierre Lafaye de Micheaux, Alexandre Leblanc. Goodness-of-fit test of normality against GEP alternatives. Joint Meeting of The Statistical Society of Canada and The Société Française de Statistique, May 2008, Ottawa, Canada. pp.232. ⟨hal-00299390⟩