Lower and upper bounds on the variances of spacings

Paweł Marcin Kozyra () and Tomasz Rychlik ()
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Paweł Marcin Kozyra: Polish Academy of Sciences
Tomasz Rychlik: Polish Academy of Sciences

Annals of the Institute of Statistical Mathematics, 2017, vol. 69, issue 2, No 7, 417-428

Abstract: Abstract For classic i.i.d. samples with an arbitrary nondegenerate and finite variance distribution, Papadatos (1995, Annals of the Institute of Statistical Mathematics, 47, 185–193) presented sharp lower and upper bounds on the variances of order statistics, expressed in population variance units. We provide here analogous results for spacings. Also, we describe the parent distributions which attain the bounds.

Keywords: Order statistic; Spacing; Variance; Sharp bound; Bernstein polynomial (search for similar items in EconPapers)
Date: 2017
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DOI: 10.1007/s10463-015-0545-6

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