A0517
Title: Exponential expansions for approximation of probability distributions
Authors: Anna Maria Gambaro - Università del Piemonte Orientale (Italy) [presenting]
Abstract: Polynomial-based expansions have been widely used in literature to approximate probability density functions. A notable example is the A-type Gram-Charlier (AGC) expansions. The AGC expansion does not guarantee the positiveness of the truncated series, which, therefore, does not constitute a valid probability density function (PDF). To encompass the above drawback, prior studies propose to approximate PDF using the C-type Gram-Charlier (CGC) expansion. This expansion is of an exponential form that always guarantees positive truncated probabilities for any degree of skewness and kurtosis of the true PDF. The existing literature is extended in two main directions. Firstly, a promising link is highlighted between the exponential expansion approach for approximating PDFs and the theory of Bayes spaces, which is extensively studied in functional statistics. In particular, novel findings are introduced concerning the convergence of this series towards the true density function, employing mathematical tools of Bayes spaces. Secondly, the moment-based estimation of the coefficients of the exponential expansion is studied. A simple linear system is proposed to estimate the expansion coefficients, given the first n exact moments of the corresponding distributions and for any orthogonal polynomial basis of the Bayes space. Finally, numerical examples are provided that effectively demonstrate the efficiency and straightforward implementability of the proposed approach.
