Abstract
It is well known that if X1, X2 are independent exponential random variables then the two corresponding spacings X1: 2 and X2: 2 − X1: 2 are independent random variables. Under mild continuity regularity conditions, such independence characterizes the possibly shifted exponential distribution. If instead, it is only assumed that the two spacings are orthogonal, a variety of non-exponential distributions can be expected to be encountered. Certain classes of distributions which do not have orthogonal spacings are described. Negatively correlated spacings appear to be most common. Several strategies are investigated for identifying distributions for which the two spacings are orthogonal. Extensions to samples of sizes greater than two are discussed.
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