Roman I. Andrushkiw, Dmitry A. Klyushin, Yuriy I. Petunin, “A new test for unimodality”, Theory Stoch. Process., 2008, Volume 14(30), Issue 1,Pages <nobr>1

A new test for unimodality

Roman I. Andrushkiw^a, Dmitry A. Klyushin^b, Yuriy I. Petunin^b

^a Department of Mathematical Sciences and Center for Applied Mathematics and Statistics, New Jersey Institute of Technology, Newark, NJ 07102, USA
^b Taras Shevchenko Kyiv National University, Department of Cybernetics, 64, Volodymyrska Str., Kyiv 01033, Ukraine

Abstract: A distribution function (d.f.) of a random variable is unimodal if there exists a number such that d.f. is convex left from this number and is concave right from this number. This number is called a mode of d.f. Since one may have more than one mode, a mode is not necessarily unique. The purpose of this paper is to construct nonparametric tests for the unimodality of d.f. based on a sample obtained from the general population of values of the random variable by simple sampling. The tests proposed are significance tests such that the unimodality of d.f. can be guaranteed with some probability (confidence level).

Keywords: Unimodality, distribution function, significance test.

MSC: 62G05

Language: English