2014/11/10 by Stephen Portnoy, Portnoy, Stephen
Mathematics · #Advanced Statistical Methods and Models #FOS: Mathematics #Statistical Distribution Estimation and Applications #Statistical Methods and Bayesian Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1411.2566
openalex publication_date 2014/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Lindsay and Basak (2000) posed the question of how far from normality could a distribution be if it matches k normal moments. They provided a bound on the maximal difference in c.d.f.'s, and implied that these bounds were attained. It will be shown here that in fact the bound is not attained if the number of even moments matched is odd. An explicit solution is developed as a symmetric distribution with a finite number of mass points when the number of even moments matched is even, and this bound for the even case is shown to hold as an explicit limit for the subsequent odd case.