Czekała, F. The asymptotic distributions of statistics based on logarithms of spacings. (English) Zbl 0805.62019 Zastosow. Mat. 21, No. 4, 511-519 (1993). Let \(V_ 1, V_ 2,\dots, V_{n+1}\) denote the \(n+1\) spacings of a random sample of size \(n\) from a density \(f\) on the interval \([0,1]\). The asymptotic distributions of \(\Sigma\log V_ i\) and \(\Sigma V_ i\log V_ i\) are obtained when \(f\) is a step function. The author’s results thus generalize those of D. A. Darling [Ann. Math. Statistics 24, 239-253 (1953; Zbl 0053.099)] and J. R. Gebert and B. K. Kale [Stat. Hefte, N. F. 10, 192-200 (1969; Zbl 0179.241)] who were concerned with the case of uniform \(f\). Reviewer: S.N.U.A.Kirmani (Cedar Falls) Cited in 3 Documents MSC: 62E20 Asymptotic distribution theory in statistics 62G30 Order statistics; empirical distribution functions 62G20 Asymptotic properties of nonparametric inference Keywords:logarithms of spacings; step function Citations:Zbl 0053.099; Zbl 0179.241 PDFBibTeX XMLCite \textit{F. Czekała}, Zastosow. Mat. 21, No. 4, 511--519 (1993; Zbl 0805.62019)