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
SN - 0004-9581
VL - 36
SP - 351
EP - 354
JO - Australian Journal of Statistics
JF - Australian Journal of Statistics
IS - 3
ER -