Related papers: A Note on a Sum of Lognormals
The higher-order statistics (HOS) of the channel capacity $\mu_n=\mathbb{E}[\log^n(1+\gamma_{end})]$, where $n\in\mathbb{N}$ denotes the order of the statistics, has received relatively little attention in the literature, due in part to the…
The present manuscript is about application of It{\^o}'s calculus to the moment-generating function of the lognormal distribution. While Taylor expansion fails when applied to the moments of the lognormal due to divergence, various methods…
CDF2PDF is a method of PDF estimation by approximating CDF. The original idea of it was previously proposed in [1] called SIC. However, SIC requires additional hyper-parameter tunning, and no algorithms for computing higher order derivative…
This article presents differential equations and solution methods for the functions of the form $Q(x) = F^{-1}(G(x))$, where $F$ and $G$ are cumulative distribution functions. Such functions allow the direct recycling of Monte Carlo samples…
Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…
Our aim in this article is to provide explicit computable estimates for the cumulative distribution function (c.d.f.) and the $p$-th order moment of the exponential functional of a fractional Brownian motion (fBM) with drift. Using…
The graph Fourier transform (GFT) is a fundamental tool in graph signal processing and has recently been extended to the graph fractional Fourier transform (GFRFT). Existing sampling methods in the GFRFT domain are primarily designed to…
We present a non-parametric joint estimation method for fMRI task activation values and the hemodynamic response function (HRF). The HRF is modeled as a Gaussian process, making continuous evaluation possible for jittered paradigms and…
Marginal model is a popular instrument for studying longitudinal data and cluster data. This paper investigates the estimator of marginal model with subgroup auxiliary information. To marginal model, we propose a new type of auxiliary…
The Gaussian graphical model (GGM) incorporates an undirected graph to represent the conditional dependence between variables, with the precision matrix encoding partial correlation between pair of variables given the others. To achieve…
A novel recurrence formula for moments with respect to M\"{u}ntz-Legendre polynomials is proposed and applied to construct a numerical method for solving generalized Gauss quadratures with power function weight for M\"{u}ntz systems. These…
We consider the problem of molecular graph generation using deep models. While graphs are discrete, most existing methods use continuous latent variables, resulting in inaccurate modeling of discrete graph structures. In this work, we…
Current fluctuations play an important role in non-equilibrium statistical mechanics, and are a key object of interest in both theoretical studies and in practical applications. So far, most of the studies were devoted to the fluctuations…
We propose non-phase-matched sum frequency generation (SFG) as a method for characterizing broadband multimode light. We demonstrate its advantages using high-gain parametric down conversion (PDC) as an example. By generating the sum…
Many developments in Mathematics involve the computation of higher order derivatives of Gaussian density functions. The analysis of univariate Gaussian random variables is a well-established field whereas the analysis of their multivariate…
In this paper, we consider some aspects of the numerical analysis of the mathematical model of fractional Duffing with a derivative of variable fractional order of the Riemann-Liouville type. Using numerical methods: an explicit…
Hansen (1982) proposed a class of "generalized method of moments" (GMMs) for estimating a vector of regression parameters from a set of score functions. Hansen established that, under certain regularity conditions, the estimator based on…
In this paper, we combine ideas from two different scientific traditions: 1) graph transformation systems (GTSs) stemming from the theory of formal languages and concurrency, and 2) mean field approximations (MFAs), a collection of…
We investigate a class of power series occurring in some problems in quantum optics. Their coefficients are either Gegenbauer or Laguerre polynomials multiplied by binomial coefficients. Although their sums have been known for a long time,…
This paper investigates an efficient exponential integrator generalized multiscale finite element method for solving a class of time-evolving partial differential equations in bounded domains. The proposed method first performs the spatial…