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A new test for unimodality. (English) Zbl 1193.62078
Summary: A distribution function (d.f.) of a random variable is unimodal if there exists a number such that the d.f. is left convex and right concave from this number. This number is called a mode of the 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.s based on a sample obtained from a general population of values of the random variable by simple sampling. The tests proposed are significance tests such that the unimodality of the d.f. can be guaranteed with some probability (confidence level).
62G10 Nonparametric hypothesis testing