In the paper, we discuss the transformation of the asymptotic expansion for the distribution of a statistic admitting Edgeworth expansion if the sample size is replaced by a random variable.We demonstrate that all those statistics that are regarded as asymptotically normal in the classical sense, become asymptotically Laplace or Student if the sample size is random. Thus, the Laplace and Studen...

We derive the asymptotic distribution of parameters Berry et al. (1995) (BLP) model in a many markets setting which takes into account simulation noise under assumption overlapping draws. show that as long number draws R and T approach infinity, our estimator is m=min(R,T) consistent asymptotically normal. do not impose any relationship between rates at go to thus allowing for case R≪T. provide...

We show a connection formula of the Hahn–Exton q-Bessel function around the origin and the infinity. We introduce the q-Borel transformation and the q-Laplace transformation following C. Zhang to obtain the connection formula. We consider the limit p→ 1− of the connection formula.

We study in distributional sense by means of the kernel method an integral transform introduced by Krätzel. It is well known that the cited transform generalizes to the Laplace and Meijer transformation. Properties of analyticity, boundedness, and inversion theorems are established for the generalized transformation. 2000 Mathematics Subject Classification. Primary 44A15, 46F12.

In this paper we investigate overdetermined systems of scalar PDEs on the plane with one common characteristic, whose general solution depends 1 function variable. We describe linearization such and their integration via Laplace transformation, relating to Lie's theorem formal theory PDEs.

A dual-reciprocity boundary element method is presented for the numerical solution of a class of axisymmetric elastodynamic problems. The domain integrals that arise in the integrodifferential formulation are converted to line integrals by using the dual-reciprocity method together suitably constructed interpolating functions. The second order time derivatives of the displacement in the governi...