A method for estimating the power of moments

Let X be an observable random variable with unknown distribution function [Formula: see text] , [Formula: see text] , and let [Formula: see text] We call θ the power of moments of the random variable X. Let [Formula: see text] be a random sample of size n drawn from [Formula: see text] . In this pap...

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Detalles Bibliográficos
Autores principales: Chang, Shuhua, Li, Deli, Qi, Yongcheng, Rosalsky, Andrew
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5840234/
https://www.ncbi.nlm.nih.gov/pubmed/29540973
http://dx.doi.org/10.1186/s13660-018-1645-7
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author Chang, Shuhua
Li, Deli
Qi, Yongcheng
Rosalsky, Andrew
author_facet Chang, Shuhua
Li, Deli
Qi, Yongcheng
Rosalsky, Andrew
author_sort Chang, Shuhua
collection PubMed
description Let X be an observable random variable with unknown distribution function [Formula: see text] , [Formula: see text] , and let [Formula: see text] We call θ the power of moments of the random variable X. Let [Formula: see text] be a random sample of size n drawn from [Formula: see text] . In this paper we propose the following simple point estimator of θ and investigate its asymptotic properties: [Formula: see text] where [Formula: see text] , [Formula: see text] . In particular, we show that [Formula: see text] This means that, under very reasonable conditions on [Formula: see text] , [Formula: see text] is actually a consistent estimator of θ.
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spelling pubmed-58402342018-03-12 A method for estimating the power of moments Chang, Shuhua Li, Deli Qi, Yongcheng Rosalsky, Andrew J Inequal Appl Research Let X be an observable random variable with unknown distribution function [Formula: see text] , [Formula: see text] , and let [Formula: see text] We call θ the power of moments of the random variable X. Let [Formula: see text] be a random sample of size n drawn from [Formula: see text] . In this paper we propose the following simple point estimator of θ and investigate its asymptotic properties: [Formula: see text] where [Formula: see text] , [Formula: see text] . In particular, we show that [Formula: see text] This means that, under very reasonable conditions on [Formula: see text] , [Formula: see text] is actually a consistent estimator of θ. Springer International Publishing 2018-03-06 2018 /pmc/articles/PMC5840234/ /pubmed/29540973 http://dx.doi.org/10.1186/s13660-018-1645-7 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Chang, Shuhua
Li, Deli
Qi, Yongcheng
Rosalsky, Andrew
A method for estimating the power of moments
title A method for estimating the power of moments
title_full A method for estimating the power of moments
title_fullStr A method for estimating the power of moments
title_full_unstemmed A method for estimating the power of moments
title_short A method for estimating the power of moments
title_sort method for estimating the power of moments
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5840234/
https://www.ncbi.nlm.nih.gov/pubmed/29540973
http://dx.doi.org/10.1186/s13660-018-1645-7
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