Moments Determine the Tail of a Distribution (But Not Much Else)

Bruce G. Lindsay; Prasanta Basak

doi:10.1080/00031305.2000.10474556

Moments Determine the Tail of a Distribution (But Not Much Else)

Bruce G. Lindsay
, Prasanta Basak

Division of Mathematics & Natural Sciences (Altoona)

Research output: Contribution to journal › Article › peer-review

45 Scopus citations

Abstract

How much information does a finite collection of moments carry about the underlying distribution? We revive an old bound, give a new, simple formula for its calculation, and demonstrate that although very little can be said about the central part of the distribution, the tail is much more sharply defined.

Original language	English (US)
Pages (from-to)	248-251
Number of pages	4
Journal	American Statistician
Volume	54
Issue number	4
DOIs	https://doi.org/10.1080/00031305.2000.10474556
State	Published - Nov 2000

All Science Journal Classification (ASJC) codes

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1080/00031305.2000.10474556

Cite this

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title = "Moments Determine the Tail of a Distribution (But Not Much Else)",

abstract = "How much information does a finite collection of moments carry about the underlying distribution? We revive an old bound, give a new, simple formula for its calculation, and demonstrate that although very little can be said about the central part of the distribution, the tail is much more sharply defined.",

author = "Lindsay, \{Bruce G.\} and Prasanta Basak",

note = "Funding Information: Bruce G. Lindsay is Distinguished Professor of Statistics, Pennsylvania State University, University Park, PA 16801. Prasanta Bas\& is Associate Professor of Mathematics, Penn State Altoona, Altoona, PA 16601 (E-mail: [email protected]). The research of Bruce G. Lindsay was partially supported by NSF Grant DMS-9403847.",

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N2 - How much information does a finite collection of moments carry about the underlying distribution? We revive an old bound, give a new, simple formula for its calculation, and demonstrate that although very little can be said about the central part of the distribution, the tail is much more sharply defined.

AB - How much information does a finite collection of moments carry about the underlying distribution? We revive an old bound, give a new, simple formula for its calculation, and demonstrate that although very little can be said about the central part of the distribution, the tail is much more sharply defined.

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SN - 0003-1305

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Moments Determine the Tail of a Distribution (But Not Much Else)

Abstract

All Science Journal Classification (ASJC) codes

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