An iterative algorithm to bound partial moments

Sander Muns

doi:10.1007/s00180-018-0825-8

An iterative algorithm to bound partial moments

Sander Muns^*

^*Corresponding author for this work

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

Abstract

This paper presents an iterative algorithm that bounds the lower and upper partial moments of an arbitrary univariate random variable X by using the information contained in a sequence of finite moments of X. The obtained bounds on the partial moments imply bounds on the moments of the transformation f(X) for a certain function f:\mathbb {R}\rightarrow \mathbb {R} . Two examples illustrate the performance of the algorithm.

Original language	English
Pages (from-to)	89-122
Journal	Computational Statistics
Volume	34
Issue number	1
DOIs	https://doi.org/10.1007/s00180-018-0825-8
Publication status	Published - Mar 2019

Keywords

Moment problem
Bounds
Censored distributions
Iteration convergence
PROBABILITY-DISTRIBUTIONS
INFORMATION
RECONSTRUCTION
EXPECTATION
TAIL

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10.1007/s00180-018-0825-8

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title = "An iterative algorithm to bound partial moments",

abstract = "This paper presents an iterative algorithm that bounds the lower and upper partial moments of an arbitrary univariate random variable X by using the information contained in a sequence of finite moments of X. The obtained bounds on the partial moments imply bounds on the moments of the transformation f(X) for a certain function f:\mathbb {R}\rightarrow \mathbb {R} . Two examples illustrate the performance of the algorithm.",

keywords = "Moment problem, Bounds, Censored distributions, Iteration convergence, PROBABILITY-DISTRIBUTIONS, INFORMATION, RECONSTRUCTION, EXPECTATION, TAIL",

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doi = "10.1007/s00180-018-0825-8",

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AB - This paper presents an iterative algorithm that bounds the lower and upper partial moments of an arbitrary univariate random variable X by using the information contained in a sequence of finite moments of X. The obtained bounds on the partial moments imply bounds on the moments of the transformation f(X) for a certain function f:\mathbb {R}\rightarrow \mathbb {R} . Two examples illustrate the performance of the algorithm.

KW - Moment problem

KW - Bounds

KW - Censored distributions

KW - Iteration convergence

KW - PROBABILITY-DISTRIBUTIONS

KW - INFORMATION

KW - RECONSTRUCTION

KW - EXPECTATION

KW - TAIL

U2 - 10.1007/s00180-018-0825-8

DO - 10.1007/s00180-018-0825-8

M3 - Article

SN - 0943-4062

VL - 34

SP - 89

EP - 122

JO - Computational Statistics

JF - Computational Statistics

IS - 1

ER -

An iterative algorithm to bound partial moments

Abstract

Keywords

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