Rounding of Continuous Random Variables and Oscillatory Asymptotics by Svante Janson
نویسنده
چکیده
We study the characteristic function and moments of the integer-valued random variable X+α , where X is a continuous random variables. The results can be regarded as exact versions of Sheppard’s correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variables. This leads to oscillatory terms in asymptotics for these variables, something that has often been observed, for example in the analysis of several algorithms. We give some examples, including applications to tries, digital search trees and Patricia tries.
منابع مشابه
Rounding of Continuous Random Variables and Oscillatory Asymptotics
We study the characteristic function and moments of the integer-valued random variable bX+αc, whereX is a continuous random variable. The results can be regarded as exact versions of Sheppard’s correction. Rounded variables of this type often occur as subsequence limits of sequences of integer-valued random variable. This leads to oscillatory terms in asymptotics for these variables, something ...
متن کاملEuler–frobenius Numbers and Rounding
We study the Euler–Frobenius numbers, a generalization of the Eulerian numbers, and the probability distribution obtained by normalizing them. This distribution can be obtained by rounding a sum of independent uniform random variables; this is more or less implicit in various results and we try to explain this and various connections to other areas of mathematics, such as spline theory. The mea...
متن کاملProbability Asymptotics: Notes on Notation
We define and compare several different versions of the O and o notations for random variables. The main purpose is to give proper definitions in order to avoid ambiguities and mistakes.
متن کاملMoments of Gamma type and the Brownian supremum process area
We study positive random variables whose moments can be expressed by products and quotients of Gamma functions; this includes many standard distributions. General results are given on existence, series expansion and asymptotics of density functions. It is shown that the integral of the supremum process of Brownian motion has moments of this type, as well as a related random variable occurring i...
متن کاملPrecise Logarithmic Asymptotics for the Right Tails of Some Limit Random Variables for Random Trees
For certain random variables that arise as limits of functionals of random finite trees, we obtain precise asymptotics for the logarithm of the right-hand tail. Our results are based on the facts (i) that the random variables we study can be represented as functionals of a Brownian excursion and (ii) that a large deviation principle with good rate function is known explicitly for Brownian excur...
متن کامل