Details

Autor(en) / Beteiligte

• Heinrich, Lothar
• Pukelsheim, Friedrich
• Wachtel, Vitali

Titel

The variance of the discrepancy distribution of rounding procedures, and sums of uniform random variables

Ist Teil von

• Metrika, 2017-04, Vol.80 (3), p.363-375

Ort / Verlag

Berlin/Heidelberg: Springer Berlin Heidelberg

Erscheinungsjahr

2017

Quelle

SpringerLink

Beschreibungen/Notizen

• When ℓ probabilities are rounded to integer multiples of a given accuracy  n , the sum of the numerators may deviate from n by a nonzero discrepancy. It is proved that, for large accuracies n → ∞ , the limiting discrepancy distribution has variance ℓ / 12 . The relation to the uniform distribution over the interval [ - 1 / 2 , 1 / 2 ] , whose variance is 1 / 12, is explored in detail.