In 1967 F. Mosteller, C. Youtz and D. Zahn in {|it ``The distribution of sums of rounded percentages''} (Demography 4, 850--858) investigated the frequence that may have the rounded percentages in order to fail to add 100 % and mostly the distributions of sums of rounded percentages in some specific cases. Later on, in 1979, P. Diaconis and D. Freedman assessed the probability that a table of rounded percentages adds to 100% by giving a mathematical treatment of this phenomenon in the case that the table is drawn from a multinomial distribution or from a mixture of multinomial distributions. M. L. Balinski and S. T. Rachev in 1992 continued their work by introducing the so-called {it stationary rules} and by considering vectors and matrices under varying assumptions regarding the probabilistic structure of the data that is to be rounded. Following the abovementioned approaches the author in {it ``Probabilistic approaches to the rounding problem''} (Serdica Bulgaricae, Mathimaticae Publicationes, 1993) examined the rounding problem under a variety of possible rounding rules and more specifically studied the vector (p,h) of rouding in the particular case where $p$ is uniformly distributed on the Simplex S_n. The aim of the present paper is to study the vector problem by modyfing the objective of rounding originally considered. In particular the author gives new results concerning with the vector problem in the case that the components of p are independent and identically distributed random variables as well as with the rounding errors of linear functions of such variables.

Στοιχεία Άρθρου

Περιοδικό	Δελτίο της Ελληνικής Μαθηματικής Εταιρίας
Αρ. Τεύχους	Τεύχος 43
Περίοδος	2000
Συγγραφέας	Bessy Dim. Athanasopoulos
Αρ. Αρθρου	1
Σελίδες	3-35
Γλώσσα	-
Λέξεις Κλειδιά	vector problem, rounding problem

A Generalized Treatment of the Rounding Problem. Rounding errors of Linear Functions