Asymptotic properties of the straight line estimator for a renewal function

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


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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.

Item Type:Article
Keywords:Asymptotic normality; asymptotic unbiasedness; consistency; nonparametric estimator; renewal function
Journal:Sains Malaysiana
ID Code:8990
Deposited By: ms aida -
Deposited On:08 Sep 2015 14:08
Last Modified:14 Dec 2016 06:48

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