 
Summary: Some new tests for normality based on
Uprocesses
Miguel A. Arcones
Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902
Yishi Wang
Department of Mathematical Sciences, Binghamton University, Binghamton, NY 13902
June 14, 2005
Abstract
We present two new tests for normality based on Uprocesses. These tests improve
on the Lilliefors tests. We obtain the consistency and asymptotic null distribution of
these tests. We present simulations of the power of these tests and of several classical
tests for some fixed alternatives. These simulations show that the presented tests are
competitive.
1 Introduction
Many statistical procedures assume that the observations are normally distributed. Hence,
testing for normality should be done before using many statistical analysis. A very complete
review of normality tests is in Thode (2002). The classical normality tests are the ones by
Lilliefors (1967) and Shapiro and Wilk (1965, 1968). Shapiro, Wilk and Chen (1968) show
that the Lilliefors test is not as powerful as the ShapiroWilk test. Several authors have
provided different approaches to test normality. Mardia (1980) reviews tests for normality
