TY - JOUR
A2 - Kalla, Shyam L.
AU - Marengo, James E.
AU - Farnsworth, David L.
AU - Stefanic, Lucas
PY - 2017
DA - 2017/09/18
TI - A Geometric Derivation of the Irwin-Hall Distribution
SP - 3571419
VL - 2017
AB - The Irwin-Hall distribution is the distribution of the sum of a finite number of independent identically distributed uniform random variables on the unit interval. Many applications arise since round-off errors have a transformed Irwin-Hall distribution and the distribution supplies spline approximations to normal distributions. We review some of the distribution’s history. The present derivation is very transparent, since it is geometric and explicitly uses the inclusion-exclusion principle. In certain special cases, the derivation can be extended to linear combinations of independent uniform random variables on other intervals of finite length. The derivation adds to the literature about methodologies for finding distributions of sums of random variables, especially distributions that have domains with boundaries so that the inclusion-exclusion principle might be employed.
SN - 0161-1712
UR - https://doi.org/10.1155/2017/3571419
DO - 10.1155/2017/3571419
JF - International Journal of Mathematics and Mathematical Sciences
PB - Hindawi
KW -
ER -