Abstract

Summary (Superposition of two frequency distributions)Notation:n: number of observationsM: arithmetic means̀: standard deviationμr: rth moment coefficientβ1: coefficient of skewnessβ2: coefficient of kurtosis.The suffixes a and b apply to the component distributions. The suffix t applies to the resulting distributions. The problem: Given the first r moments of two frequency distributions (to begin with μ0). Find the first r moments of the distribution resulting from superposition of the two components (r≥5).Formulae [1]. … [5] (§3) give the results in their most general form up to μ4.Some special cases are treated in § 4, and eight different cases of superposition of two normal distributions in § 5.In § 6 some remarks are made about the reverse situation, i.e. the splitting into two normal components of a combined frequency distribution.

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