Mathematics and Statistics Vol. 5(4), pp. 151 - 163
DOI: 10.13189/ms.2017.050403
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Nonparametric Estimation of Replacement Rates

Nora Dörmann *
University of Duisburg-Essen, Germany


Let Xi, i ≥ 1, describe the lifetimes of items with finite mean μ = E (Xi) which are successively placed in service. In order to estimate the replacement rate 1/μ or related quantities, the random variables Xi are usually assumed to be independent and identically distributed. It is shown that a nonparametric estimation of the replacement rate and other reciprocal functions of renewal theory is possible while using a delta method with weakened requirements upon the global growth of f which also allows dependent observations and respects the unboundedness of the analyzed reciprocal functions. Moreover, results on the moments and, furthermore, on corresponding simulations are included.

Rate of Replacement, Elementary Renewal Theorem, Delta Method, Weak Law of Large Numbers, Asymptotic Expansion of Moments, Dependent Observations

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Nora Dörmann , "Nonparametric Estimation of Replacement Rates," Mathematics and Statistics, Vol. 5, No. 4, pp. 151 - 163, 2017. DOI: 10.13189/ms.2017.050403.

(b). APA Format:
Nora Dörmann (2017). Nonparametric Estimation of Replacement Rates. Mathematics and Statistics, 5(4), 151 - 163. DOI: 10.13189/ms.2017.050403.