Superpositie van twee frequentieverdelingen

J. Sittig

Statistica Neerlandica, 1948, vol. 2, issue 5‐6, 206-227

Abstract: Summary (Superposition of two frequency distributions) Notation: n: number of observations M: arithmetic mean s̀: standard deviation μr: rth moment coefficient β1: coefficient of skewness β2: 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.

Date: 1948
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