Determining Source Cumulants in Femtoscopy With Gram–charlier and Edgeworth Series

Abstract

Lowest-order cumulants provide important information on the shape of the emission source in femtoscopy. For the simple case of noninteracting identical particles, we show how the fourth-order source cumulant can be determined from measured cumulants in momentum space. The textbook Gram-Charlier series is found to be highly inaccurate, while the related Edgeworth series provides increasingly accurate estimates. Ordering of terms compatible with the Central Limit Theorem appears to play a crucial role even for nongaussian distributions.

Option Pricing with the Realized GARCH Model: An Analytical Approximation Approach

“…Cramér compared the two expansion in a series of papers, and deemed the Edgeworth expansion to be superior, see, for example, Cramér (). Formally, when a Gaussian distribution is employed as reference distribution, Blinnikov and Moessner () show that the Edgeworth expansion achieves a better approximation for near‐Gaussian distribution, and Eggers, de Kock, and Schmiegel () highlights how poorly the Gram–Charlier expansion is at approximating a symmetric Normal Inverse Gaussian distribution, while the Edgeworth expansion performs well.…”

From chi^2 to Bayesian model comparison: the example of Levy-based fits to e+e- correlations

“…It may be helpful to use them, as we have done here, merely as part of parametrisations of data to which they show some resemblance. More systematic use in Gram-Charlier or other expansions will be faced with issues inherent in all asymptotic series [7,8].…”