On the computation of classical, boolean and free cumulants

Applied Mathematics and Computation

Volumn 208, Issue 2, 2009, Pages 347-354

  Di Nardo, E ^a   Oliva, I ^b  

^a UNIVERSITY OF BASILICATA   (Italy)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Abel polynomial; Boolean cumulant; Classical cumulant; Free cumulant; Umbral calculus

Indexed keywords

POLYNOMIAL APPROXIMATION; POLYNOMIALS;

ABEL POLYNOMIAL; BOOLEAN CUMULANT; CLASSICAL CUMULANT; FREE CUMULANT; UMBRAL CALCULUS;

CALCULATIONS;

EID: 59149092903     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.11.047     Document Type: Article

References (15)

1. Bryc W. Computing moments of free additive convolution of measures. Appl. Math. Comp. 194 (2007) 561-567
2. McCullagh P. Tensor methods in statistics. Monographs on Statistics and Applied Probability (1987), Chapman & Hall, London
3. Di Nardo E., and Senato D. Umbral nature of the Poisson random variables. Algebraic Combinatorics and Computer Science (2001), Springer Italia, Milan pp. 245-266
4. Di Nardo E., and Senato D. An umbral setting for cumulants and factorial moments. Eur. J. Combin. 27 3 (2006) 394-413
5. Di Nardo E., Guarino G., and Senato D. A unifying framework for k-statistics, polykays and their multivariate generalizations. Bernoulli 14 2 (2008) 440-468
6. Di Nardo E., Guarino G., and Senato D. Symbolic computation of moments of sampling distributions. Comput. Stat. Data Anal. 52 11 (2008) 4909-4922
7. E. Di Nardo, G. Guarino, D. Senato, A new method for fast computing unbiased estimators of cumulants, Stat. Comp. in press, doi:10.1007/s11222-008-9080-0.
8. E. Di Nardo, P. Petrullo, D. Senato, Cumulants, convolutions and volume polynomials, submitted for publication.
9. Feller W. An Introduction to Probability Theory and its Applications vol. II (1966), John Wiley & Sons, New York
10. Roman S.M., and Rota G.-C. The umbral calculus. Adv. Math. 27 (1978) 95-188
11. Rota G.-C., and Taylor B.D. The classical umbral calculus. SIAM J. Math. Anal. 25 2 (1994) 694-711
12. Speicher R. Multiplicative functions on the lattice of non-crossing partitions and free convolution. Math. Ann. 298 (1994) 611-628
13. Speicher R. Free probability theory and non-crossing partitions. Sém. Loth. Combin. B39c (1997)
14. R. Speicher, R. Woroudi, Boolean convolution, in: D. Voiculescu, (Ed.), Fields Inst. Commun., vol. 12, 1997, pp. 267-279.
15. Voiculescu D. Addition of certain non-commuting random variables. J. Funct. Anal. 66 (1986) 323-346