Premium
Discrete Spacings
Author(s) -
Klaassen Chris A.J.,
Theo Runnenburg J.
Publication year - 2003
Publication title -
statistica neerlandica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.52
H-Index - 39
eISSN - 1467-9574
pISSN - 0039-0402
DOI - 10.1111/1467-9574.00240
Subject(s) - mathematics , limiting , string (physics) , combinatorics , distribution (mathematics) , mathematical analysis , geometry , mathematical physics , mechanical engineering , engineering
Consider a string of n positions, i.e. a discrete string of length n . Units of length k are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring units have length less than k . When centered and scaled by n −1/2 the resulting numbers of spacings of length 1, 2,…, k −1 have simultaneously a limiting normal distribution as n →∞. This is proved by the classical method of moments.