# Limiting distributions of homogeneous functions of sample spacings for distributions approaching the uniform distribution

Research paper by Lionel Weiss

Indexed on: 01 Sep '68Published on: 01 Sep '68Published in: Probability Theory and Related Fields

#### Abstract

X1,...,Xn are independent random variables, identically distributed over the unit interval, with common probability density function 1 + r(x)/nδ for all sufficiently large n, where δ is a positive constant, $$\int\limits_0^1 {r(x){\text{ }}dx = 0}$$ and |r″(x)| <D. V1, ..., Vn+1 are the sample spacings generated by X1,..., Xn. It is shown that in many cases, the asymptotic joint distribution of homogeneous functions of V1,..., Vn+1 can be found directly from the asymptotic joint distribution of homogeneous functions of independent exponential random variables.