Quasinormal distributions and expansion at the mode

Tomozawa, Yukio

doi:10.1007/BF01010217

Quasinormal distributions and expansion at the mode

Journal Article · Sun Sep 01 00:00:00 EDT 1974 · Journal of Statistical Physics

DOI:https://doi.org/10.1007/BF01010217· OSTI ID:1442839

Tomozawa, Yukio ^[1]

Univ. of Michigan, Ann Arbor, MI (United States). Randall Lab. of Physics; SLAC National Accelerator Lab., Menlo Park, CA (United States)

The Gram-Charlier series of type A is discussed here in terms ofdeviants which are related to moments in a way similar to the way Hermite polynomials are related to the powers. Distribution functions are also expressed in terms of the mode and moments (cumulants or deviants), which are useful expansions when the distributions are approximately normal. It is shown that such expansions as well as the Gram-Charlier series are valid asymptotically for discrete distributions defined on the semiinfinite interval [0, ∞].

Research Organization:: SLAC National Accelerator Lab., Menlo Park, CA (United States); Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Organization:: US Atomic Energy Commission (AEC)

Grant/Contract Number:: AC02-76SF00515

OSTI ID:: 1442839

Alternate ID(s):: OSTI ID: 7320740

Report Number(s):: SLAC-PUB--1233

Journal Information:: Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 3 Vol. 11; ISSN 0022-4715

Publisher:: SpringerCopyright Statement

Country of Publication:: United States

Language:: English

References (7)

The 200 GeV multiplicity distribution and scaling Olesen, P. Physics Letters B, Vol. 41, Issue 5 https://doi.org/10.1016/0370-2693(72)90644-2	journal	October 1972
A new model for particle multiplicities in strong interaction production processes Kaiser, G. D. Nuclear Physics B, Vol. 44, Issue 1 https://doi.org/10.1016/0550-3213(72)90278-7	journal	July 1972
Multiplicity distribution in high energy collisions Tomozawa, Yukio Nuclear Physics B, Vol. 62 https://doi.org/10.1016/0550-3213(73)90269-1	journal	October 1973
The mode and Median of a Nearly Normal Distribution with Given Cumulants Haldane, J. B. S. Biometrika, Vol. 32, Issue 3-4 https://doi.org/10.1093/biomet/32.3-4.294	journal	January 1942
Evidence for the Systematic Behavior of Charged-Prong Multiplicity Distributions in High-Energy Proton-Proton Collisions Slattery, P. Physical Review D, Vol. 7, Issue 7 https://doi.org/10.1103/PhysRevD.7.2073	journal	April 1973
Asymptotic Multiplicity Distributions and Analog of the Central-Limit Theorem Tomozawa, Yukio Physical Review D, Vol. 8, Issue 7 https://doi.org/10.1103/PhysRevD.8.2138	journal	October 1973
Moments and Cumulants in the Specification of Distributions Cornish, E. A.; Fisher, R. A. Revue de l'Institut International de Statistique / Review of the International Statistical Institute, Vol. 5, Issue 4 https://doi.org/10.2307/1400905	journal	January 1938

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M-estimation with probabilistic models of geodetic observations Wiśniewski, Z. Journal of Geodesy, Vol. 88, Issue 10 https://doi.org/10.1007/s00190-014-0735-7	journal	June 2014

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Gram-Charlier series of type A
cumulants
deviants
mode
moments
quasinormal expansion

Quasinormal distributions and expansion at the mode

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References (7)

Cited By (1)

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