A new formulation of the Gram-Charlier method: Performance for fitting non-normal distribution

Pelliccioni, A. and Angeloni, M. (2007) A new formulation of the Gram-Charlier method: Performance for fitting non-normal distribution. Il nuovo cimento C, 30 (4). pp. 381-394. ISSN 1826-9885

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The Gram-Charlier expansion was derived in an attempt to express non-normal densities as infinite series involving the normal density and its derivatives, using the moments data as input terms. In classic Gram-Charlier expansion the random variable is standardized, so that the Gaussian parameters are Always fixed and referred to the mean equal to zero and to the standard deviation equal to one. This assumption seems to be too strong. An improvement of Gram-Charlier expansion was obtained by an optimization process, directed to choose new values of Gaussian parameters. In order to check the performance of the new approach, an estimate of the gamma probability density function was calculated. Two probability density functions, characterized by a different degree of skewness and kurtosis, were considered. The study has shown that in comparison with the classic assumption, the new one always gives the best results in terms of probability density function reproducibility and allows the best evaluation of the input moments. Further the comparison between estimated moments of order higher than the input ones and the theoretical moments shows a good reproduction. Finally the method seems to suggest that a less restrictive condition can be considered respect to the usual convergence criterium of the Gram-Charlier expansion.

Item Type: Article
Uncontrolled Keywords: Approximations and expansions ; Probability theory ; Distribution theory and Monte Carlo studies
Subjects: 500 Scienze naturali e Matematica > 530 Fisica
Depositing User: Marina Spanti
Date Deposited: 20 Mar 2020 16:56
Last Modified: 20 Mar 2020 16:56
URI: http://eprints.bice.rm.cnr.it/id/eprint/16265

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