The existence of the first negative moment

Walter W. Piegorsch; George Casella

doi:10.1080/00031305.1985.10479390

The existence of the first negative moment

Walter W. Piegorsch, George Casella

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

33 Scopus citations

Abstract

The question of the existence of negative moments of a continuous probability density function is explored. A sufficient condition for the existence of the first negative moment is given. The condition is easy to verify, as it involves limits rather than integrals. An example is given, however, that shows that this simple condition is not necessary for the existence of the first negative moment. The delicacy of the characterization of existence is explored further with some results concerning the existence of moments surrounding the first negative moment.

Original language	English (US)
Pages (from-to)	60-62
Number of pages	3
Journal	American Statistician
Volume	39
Issue number	1
DOIs	https://doi.org/10.1080/00031305.1985.10479390
State	Published - Feb 1985
Externally published	Yes

Keywords

Inverse moment
Limit conditions
Sufficient conditions

ASJC Scopus subject areas

Statistics and Probability
General Mathematics
Statistics, Probability and Uncertainty

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10.1080/00031305.1985.10479390

Cite this

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title = "The existence of the first negative moment",

abstract = "The question of the existence of negative moments of a continuous probability density function is explored. A sufficient condition for the existence of the first negative moment is given. The condition is easy to verify, as it involves limits rather than integrals. An example is given, however, that shows that this simple condition is not necessary for the existence of the first negative moment. The delicacy of the characterization of existence is explored further with some results concerning the existence of moments surrounding the first negative moment.",

keywords = "Inverse moment, Limit conditions, Sufficient conditions",

author = "Piegorsch, \{Walter W.\} and George Casella",

note = "Funding Information: *Walter w. Piegorsch is Mathematical Statistician, Biometry and Risk Assessment Program, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, and George Casella is Associate Professor, Biometrics Unit, Cornell University, Ithaca, NY 14853. This work was performed while the first author was at Cornell University. The second author's research was supported by National Science Foundation Grant MCS81-02541. The authors wish to thank the associate editor and referees for their helpful comments.",

year = "1985",

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doi = "10.1080/00031305.1985.10479390",

language = "English (US)",

volume = "39",

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journal = "American Statistician",

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T1 - The existence of the first negative moment

AU - Piegorsch, Walter W.

AU - Casella, George

N1 - Funding Information: *Walter w. Piegorsch is Mathematical Statistician, Biometry and Risk Assessment Program, National Institute of Environmental Health Sciences, Research Triangle Park, NC 27709, and George Casella is Associate Professor, Biometrics Unit, Cornell University, Ithaca, NY 14853. This work was performed while the first author was at Cornell University. The second author's research was supported by National Science Foundation Grant MCS81-02541. The authors wish to thank the associate editor and referees for their helpful comments.

PY - 1985/2

Y1 - 1985/2

N2 - The question of the existence of negative moments of a continuous probability density function is explored. A sufficient condition for the existence of the first negative moment is given. The condition is easy to verify, as it involves limits rather than integrals. An example is given, however, that shows that this simple condition is not necessary for the existence of the first negative moment. The delicacy of the characterization of existence is explored further with some results concerning the existence of moments surrounding the first negative moment.

AB - The question of the existence of negative moments of a continuous probability density function is explored. A sufficient condition for the existence of the first negative moment is given. The condition is easy to verify, as it involves limits rather than integrals. An example is given, however, that shows that this simple condition is not necessary for the existence of the first negative moment. The delicacy of the characterization of existence is explored further with some results concerning the existence of moments surrounding the first negative moment.

KW - Inverse moment

KW - Limit conditions

KW - Sufficient conditions

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The existence of the first negative moment

Abstract

Keywords

ASJC Scopus subject areas

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