Distribution theory and inference for polynomial-normal density functions. Communications i【荐】.pdfVIP

Distribution Theory and Inference for PolynomialNormal Densities M Evans Department of Statistics University of Toronto Toronto Ontario MS A T Swartz Department of Mathematics and Statistics Simon Fraser University Burnaby British Columbia VA S Key Words and Phrases p olynomialnormal densities distribution theory conditional inference GramCharlier approximations importance sampling ABSTRACT This pap er considers a class of densities formed by taking the pro duct of nonnegative p olynomials and normal densities These densities provide a rich class of distributions that can b e used in mo delling when faced with nonnormal characteristics such as skewness and multimo dality In this pap er we address inferential and computational issues arising in the practical implementation of this parametric family in the context of the linear mo del Exact results are recorded for the conditional analysis of lo cationscale mo dels and an imp or tance sampling algorithm is develop ed for the implementation of a conditional analysis for the general linear mo del when using p olynomialnormal distribu tions for the error INTRODUCTION Parametric statistical inference often relies on an assumption of normality for an error distribution This assumption although supp orted by the Central Limit Theorem is widely recognized as articial It would therefore b e useful if there were a family of distributions that could b e used in applied problems to mo del a variety of nonnormal shap es and for which exact as opp osed to asymptotic inferences