TY - JOUR

T1 - Characterizations of shift-invariant distributions based on summation modulo one

AU - Wilms, R.J.G.

AU - Thiemann, J.G.F.

PY - 1994

Y1 - 1994

N2 - Let X1Y1,…, Yn be independent random variables. We characterize the distributions of X and Yj satisfying the equation {X+Y1++Yn}=dX, where {Z} denotes the fractional part of a random variable Z. In the case of full generality, either X is uniformly distributed on [0,1), or Yj has.a shifted lattice distribution and X is shift‐invariant. We also give a characterization of shift‐invariant distributions. Finally, we consider some special cases of this equation.

AB - Let X1Y1,…, Yn be independent random variables. We characterize the distributions of X and Yj satisfying the equation {X+Y1++Yn}=dX, where {Z} denotes the fractional part of a random variable Z. In the case of full generality, either X is uniformly distributed on [0,1), or Yj has.a shifted lattice distribution and X is shift‐invariant. We also give a characterization of shift‐invariant distributions. Finally, we consider some special cases of this equation.

U2 - 10.1111/j.1467-842X.1994.tb00887.x

DO - 10.1111/j.1467-842X.1994.tb00887.x

M3 - Article

VL - 36

SP - 351

EP - 354

JO - Australian Journal of Statistics

JF - Australian Journal of Statistics

SN - 0004-9581

IS - 3

ER -