Charlier configurations provide a combinatorial model for Charlier polynomials. We use this model to give a combinatorial proof of a multilinear generating function for Charlier polynomials. As special cases of the multilinear generating function, we obtain the bilinear generating function for Charlier polynomials and formulas for derangements.

This work aims at proposing a higher-order moments analysis, in order to obtain an effective characterisation (in a Non-Gaussian sense) of the global DS/CDMA noise in case of few-user systems and short spreading codes. The use of the Edgeworth series expansion, whose terms are directly linked with the statistical cumulants allows to reach a good approximation of the unknown probability density ...

This paper presents two new sets of nonseparable discrete orthogonal Charlier and Meixner moments describing the images with noise and that are noise-free. The basis functions used by the proposed nonseparable moments are bivariate Charlier or Meixner polynomials introduced by Tratnik et al. This study discusses the computational aspects of discrete orthogonal Charlier and Meixner polynomials, ...

This paper proposes a method for probabilistic load flow in networks with wind generation, where the uncertainty of the production is non-Gaussian. The method is based on the properties of the cumulants of the probability density functions (PDF) and the Cornish–Fisher expansion, which is more suitable for non-Gaussian PDF than other approaches, such as Gram–Charlier series. The paper includes e...

In this paper we develop an explicit formula that allows us to compute the first k moments of the random count of a pattern in a multistate sequence generated by aMarkov source. We derive efficient algorithms that allow us to deal with any pattern (low or high complexity) in any Markov model (homogeneous or not). We then apply these results to the distribution of DNA patterns in genomic sequenc...

In this paper, we develop an explicit formula allowing to compute the first k moments of the random count of a pattern in a multi-states sequence generated by a Markov source. We derive efficient algorithms allowing to deal both with low or high complexity patterns and either homogeneous or heterogenous Markov models. We then apply these results to the distribution of DNA patterns in genomic se...

A scanning-laser glint meter designed for field measurements of sea-surface slope statistics is described. A narrow laser beam is scanned in a line, and specular reflections (glints) are counted in bins according to their slope angle. From normalized glint histograms, moments to the fourth order are calculated, and slope probability density functions are approximated with a Gram-Charlier expans...

We derive a rst-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D diierential entropy is derived. The approximation...

We derive a first-order approximation of the density of maximum entropy for a continuous 1-D random variable, given a number of simple constraints. This results in a density expansion which is somewhat similar to the classical polynomial density expansions by Gram-Charlier and Edgeworth. Using this approximation of density, an approximation of 1-D differential entropy is derived. The approximat...

A new on-line learning algorithm which minimizes a statistical dependency among outputs is derived for blind separation of mixed signals. The dependency is measured by the average mutual information (MI) of the outputs. The source signals and the mixing matrix are unknown except for the number of the sources. The Gram-Charlier expansion instead of the Edgeworth expansion is used in evaluating t...