Abstract
Let U-1, U-2,..., Un-1 be an ordered sample from a Uniform [0,1] distribution. The non-overlapping uniform spacings of order s are defined as G(i)((s)) = U-is - U(i-1)s, i = 1, 2,..., N', G(N'+1)((s)) = 1 - U-N's with notation U-0 = 0, U-n = 1, where N' = inverted right perpendicularn/sinverted left perpendicular is the integer part of n/s. Let N = inverted right perpendicularn/sinverted left perpendicular be the smallest integer greater than or equal to n/s, f(m)(u), m = 1, 2,..., N, be a sequence of real-valued Borel-measurable functions. In this article a Cramer type large deviation theorem for the statistic f(1, n)(nG(1)((s)))+ ... + f(N, n)(nG(N)(s)) is proved.