Rounding of Continuous Random Variables and Oscillatory Asymptotics
نویسندگان
چکیده
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 that often has 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 by Svante Janson
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, somethin...
متن کاملRounding effects in record statistics.
We analyze record-breaking events in time series of continuous random variables that are subsequently discretized by rounding to integer multiples of a discretization scale Δ>0. Rounding leads to ties of an existing record, thereby reducing the number of new records. For an infinite number of random variables that are drawn from distributions with a finite upper limit, the number of discrete re...
متن کاملThe ∂ Steepest Descent Method for Orthogonal Polynomials on the Real Line with Varying Weights
We obtain Plancherel-Rotach type asymptotics valid in all regions of the complex plane for orthogonal polynomials with varying weights of the form e−NV (x) on the real line, assuming that V has only two Lipschitz continuous derivatives and that the corresponding equilibrium measure has typical support properties. As an application we extend the universality class for bulk and edge asymptotics o...
متن کاملAsymptotic Cost of Cutting Down Random Free Trees
In this work, we calculate the limit distribution of the total cost incurred by splitting a tree selected at random from the set of all finite free trees. This total cost is considered to be an additive functional induced by a toll equal to the square of the size of tree. The main tools used are the recent results connecting the asymptotics of generating functions with the asymptotics of...
متن کاملBernstein-like Concentration and Moment Inequalities for Polynomials of Independent Random Variables: Multilinear Case
Polynomials of independent random variables arise in a variety of fields such as Machine Learning, Analysis of Boolean Functions, Additive Combinatorics, Random Graphs Theory, Stochastic Partial Differential Equations etc. They naturally model the expected value of objective function (or lefthand side of constraints) for randomized rounding algorithms for non-linear optimization problems where ...
متن کامل