Asymptotic properties of the straight line estimator for a renewal function

In estimation problems in renewal function, when the distribution is not known, nonparametric estimators of renewal function are used. Frees (1986a, Warranty analysis and renewal function estimation, Naval Res. Logist. Quart, 33, 361-372) proposed the nonparametric estimator of renewal function for...

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Main Authors:	Gökpınar, Esra, Khaniyev, Tahir, Gamgam, Hamza
Format:	Article
Language:	English
Published:	Universiti Kebangsaan Malaysia 2015
Online Access:	http://journalarticle.ukm.my/8990/ http://journalarticle.ukm.my/8990/ http://journalarticle.ukm.my/8990/1/17_Esra_Gokpinar.pdf

id	ukm-8990
recordtype	eprints
spelling	ukm-89902016-12-14T06:48:38Z http://journalarticle.ukm.my/8990/ Asymptotic properties of the straight line estimator for a renewal function Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza In estimation problems in renewal function, when the distribution is not known, nonparametric estimators of renewal function are used. Frees (1986a, Warranty analysis and renewal function estimation, Naval Res. Logist. Quart, 33, 361-372) proposed the nonparametric estimator of renewal function for large values of t. Frees’s estimator is easy to apply in practice. It is a preferred estimator for large values of t. However, its statistical properties still have not been investigated in detailed. For this reason, in this study, we investigate asymptotic properties of this estimator such as consistency, asymptotic unbiasedness and asymptotic normality. Also Monte Carlo simulation study is given to assess the performance of this estimator according to value of renewal function. Simulation results indicate that in the large values of t, Frees estimator is sufficiently close to the renewal function for the Gamma distribution with various parameters. Universiti Kebangsaan Malaysia 2015-07 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/8990/1/17_Esra_Gokpinar.pdf Gökpınar, Esra and Khaniyev, Tahir and Gamgam, Hamza (2015) Asymptotic properties of the straight line estimator for a renewal function. Sains Malaysiana, 44 (7). pp. 1041-1051. ISSN 0126-6039 http://www.ukm.my/jsm/malay_journals/jilid44bil7_2015/KandunganJilid44Bil7_2015.html
repository_type	Digital Repository
institution_category	Local University
institution	Universiti Kebangasaan Malaysia
building	UKM Institutional Repository
collection	Online Access
language	English
description	In estimation problems in renewal function, when the distribution is not known, nonparametric estimators of renewal function are used. Frees (1986a, Warranty analysis and renewal function estimation, Naval Res. Logist. Quart, 33, 361-372) proposed the nonparametric estimator of renewal function for large values of t. Frees’s estimator is easy to apply in practice. It is a preferred estimator for large values of t. However, its statistical properties still have not been investigated in detailed. For this reason, in this study, we investigate asymptotic properties of this estimator such as consistency, asymptotic unbiasedness and asymptotic normality. Also Monte Carlo simulation study is given to assess the performance of this estimator according to value of renewal function. Simulation results indicate that in the large values of t, Frees estimator is sufficiently close to the renewal function for the Gamma distribution with various parameters.
format	Article
author	Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza
spellingShingle	Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza Asymptotic properties of the straight line estimator for a renewal function
author_facet	Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza
author_sort	Gökpınar, Esra
title	Asymptotic properties of the straight line estimator for a renewal function
title_short	Asymptotic properties of the straight line estimator for a renewal function
title_full	Asymptotic properties of the straight line estimator for a renewal function
title_fullStr	Asymptotic properties of the straight line estimator for a renewal function
title_full_unstemmed	Asymptotic properties of the straight line estimator for a renewal function
title_sort	asymptotic properties of the straight line estimator for a renewal function
publisher	Universiti Kebangsaan Malaysia
publishDate	2015
url	http://journalarticle.ukm.my/8990/ http://journalarticle.ukm.my/8990/ http://journalarticle.ukm.my/8990/1/17_Esra_Gokpinar.pdf
first_indexed	2023-09-18T19:53:42Z
last_indexed	2023-09-18T19:53:42Z
_version_	1777406388685766656

Asymptotic properties of the straight line estimator for a renewal function

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