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Title: Asymptotic Properties of the Straight Line Estimator for a Renewal Function
Authors: Gökpınar, Esra
Khaniyev, Tahir
Gamgam, Hamza
Keywords: Asymptotic normality
asymptotic unbiasedness
nonparametric estimator
renewal function
Issue Date: Jul-2015
Publisher: Univ Kebangsaan Malaysia
Source: Gökpınar, E., Khaniyev, T., & Gamgam, H. (2015). Asymptotic Properties of the Straight Line Estimator for a Renewal Function. Sains Malaysiana, 44(7), 1041-1051.
Abstract: 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.
[Gokpinar, Esra; Gamgam, Hamza] Gazi Univ, Dept Stat, TR-06500 Ankara, Turkey; [Khaniyev, Tahir] TOBB Univ Econ & Technol, Dept Ind Engn, TR-06500 Ankara, Turkey; [Khaniyev, Tahir] Natl Acad Sci, Inst Cybernet Azerbaijan, AZ-1141 Baku, Azerbaijan
ISSN: 0126-6039
Appears in Collections:Endüstri Mühendisliği Bölümü / Department of Industrial Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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