the purpose of this paper is to provide some asymptotic results for nonparametric estimator of the lorenz curve and lorenz process for the case in which data are assumed to be strong mixing subject to random left truncation. first, we show that nonparametric estimator of the lorenz curve is uniformly strongly consistent for the associated lorenz curve. also, a strong gaussian approximation for ...

This paper describes a hybrid method combining the method of moments (MM) with asymptotic current expansions for the higher frequency range. The physical optics (PO) approximation represents such an asymptotic current expansion which is rather simple to apply. However, for flat polygonal scatterers or scattering bodies containing wedge–like elements, the accuracy is improved by taking into acco...

in this article, by using chebyshev’s polynomials and chebyshev’s expansion, we obtain the best uniform polynomial approximation out of p2n to a class of rational functions of the form (ax2+c)-1 on any non symmetric interval [d,e]. using the obtained approximation, we provide the best uniform polynomial approximation to a class of rational functions of the form (ax2+bx+c)-1 for both cases b2-4a...

SUMMARY This paper investigates the finite sample distribution of the least squares estimator of the autoregressive parameter in a first-order autoregressive model. Uniform asymptotic expansion for the distribution applicable to both stationary and nonstationary cases is obtained. Accuracy of the approximation to the distribution by a first few terms of this expansion is then investigated. It i...

We introduce new diffuse approximations of the Willmore functional and flow. They are based on a corresponding approximation perimeter that has been studied by Amstutz-van Goethem [Interfaces Free Bound. 14 (2012)]. identify candidate for Γ-convergence, prove Γ-limsup statement justify convergence to flow an asymptotic expansion. Furthermore, we present numerical simulations approximation.

A nonlinear equation describing curved stationary flames with arbitrary gas expansion θ = ρfuel/ρburnt, subject to the Landau-Darrieus instability, is obtained in a closed form without an assumption of weak nonlinearity. It is proved that in the scope of the asymptotic expansion for θ → 1, the new equation gives the true solution to the problem of stationary flame propagation with the accuracy ...

An asymptotic representation of low-frequency dynamic tides in close binaries is developed. The dynamic tides are treated as low-frequency, linear, isentropic, forced oscillations of a non-rotating spherically symmetric star. The asymptotic representation is developed to the second order in the forcing frequency. For the sake of simplification, the star is assumed to be everywhere in radiative ...

Abstract Asymptotic expansion is presented for an estimator of the Hurst coefficient a fractional Brownian motion. We first derive formula principal term error using recently developed theory asymptotic distribution Wiener functionals, and utilize perturbation method on obtained in order to calculate estimator. also discuss some second-order modifications Numerical results show that attains hig...

The Barnes double gamma function G(z) is considered for large argument z. A new integral representation is obtained for log G(z). An asymptotic expansion in decreasing powers of z and uniformly valid for |Arg z|<? is derived from this integral. The expansion is accompanied by an error bound at any order of the approximation. Numerical experiments show that this bound is very accurate for real z...

Oscillatory integrals are present in many applications, and their numerical approximation is the subject of this paper. Contrary to popular belief, their computation can be achieved efficiently, and in fact, the more oscillatory the integral, the more accurate the approximation. We review several existing methods, including the asymptotic expansion, Filon method, Levin collocation method and nu...