Asymptotic expansions for conditional moments of Bernoulli trials

Asymptotic expansions of moments and cumulants

Many parameters may be expanded as series with terms involving products of expectations and their estimates expanded as series involving products of averages. The computation of moments and cu-mulants of such estimates may be organized if the terms of the series expansions of parameters, estimates and their moments are considered as functions applied to lists. The lists form a vectors space ass...

Asymptotic Expansions for Integrals

Asymptotic expansions for factorial moments of some distributions in the analysis of algorithms

We establish asymptotic expansions for factorial moments of following distributions: number of cycles in a random permutation, number of inversions in a random permutation, and number of comparisons used by the randomized quick sort algorithm. To achieve this we use singularity analysis of certain type of generating functions due to Flajolet and Odlyzko.

Asymptotic Expansions

Asymptotic expansions of functions are useful in statistics in three main ways. Firstly, conventional asymptotic expansions of special functions are useful for approximate computation of integrals arising in statistical calculations. An example given below is the use of Stirling's approximation to the gamma function. Second, asymptotic expansions of density or distribution functions of estimato...

Asymptotic Expansions for Nonlocal Diffusion

We study the asymptotic behavior for solutions to nonlocal diffusion models of the form ut = J ∗ u − u in the whole R with an initial condition u(x, 0) = u0(x). Under suitable hypotheses on J (involving its Fourier transform) and u0, it is proved an expansion of the form ∥∥u(u)− ∑ |α|≤k (−1)|α| α! ( ∫ u0(x)x dx ) ∂Kt ∥∥ Lq(Rd) ≤ Ct−A, where Kt is the regular part of the fundamental solution and...