The Gram-Charlier method to evaluate the probability density function in monodimensional case

Pelliccioni, A. (1997) The Gram-Charlier method to evaluate the probability density function in monodimensional case. Il nuovo cimento C, 20 C (3). pp. 435-452. ISSN 1826-9885

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In many experimental applications, starting from a random variable, it is possible to evaluate the moments and to define the probability density function(PDF) in different ways. In this paper a new approach is shown in order to estimate the PDF by moments according to Gram-Charlier method (GCm). The approach consists of a choice of standard deviation (s new) in GCm which optimizes the values of the input moments. In particular three s new are selected in order to minimize: 1) the sum of absolute relative deviations among theoretical and experimental moments; 2) the relative per cent of negative probabilities coming from GC expansion; 3) the product between the two previous functions. A theoretical application of the above approach is made where the input moments data set comes from the vertical velocity distribution estimated for one level of the convective mixed layer. This application consists of two different simulations. The first evaluates the moments up to 10th order, having as input data the moments up to 3rd order. The second gives the moments up to 10th order considering both the moments of the previous simulation and the 4th-order moment calculated with Gaussian closure as input data.

Item Type: Article
Additional Information: Paper presented at EUROMECH Colloquium 338 “Atmospheric Turbulence and Dispersion in Complex Terrain” and ERCOFTAC Workshop “Data on Turbulence and Dispersion in Complex Atmospheric Flows”, Bologna, 4-7 September 1995.
Uncontrolled Keywords: Boundary layer structure and processes; turbulent flows, convection, and heat transfer; conference proceedings
Subjects: 500 Scienze naturali e Matematica > 530 Fisica
Depositing User: Marina Spanti
Date Deposited: 06 Feb 2018 10:13
Last Modified: 06 Feb 2018 10:13

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