A contribution to results on random partitions of the segment. (English) Zbl 1059.62051
The division of the interval \((0,1)\) into \(k\) subintervals by \(k-1\) independent and identically distributed uniform variables is called a spacing. Let \(r(k)\) and \(R(k)\), respectively, be the smallest and the largest subinterval in such a spacing. The authors derive a number of formulas for the moments of \(r(k), R(k), R(k)-r(k)\) and \(r(k)/R(k)\). Additional results are established when the division of \((0,1)\) is made by a Poisson process.
Reviewer: Janos Galambos (Philadelphia)
MSC:
62G30 | Order statistics; empirical distribution functions |
60F15 | Strong limit theorems |
62E15 | Exact distribution theory in statistics |
60K05 | Renewal theory |
60F25 | \(L^p\)-limit theorems |