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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| Format: | Article |
| Language: | English |
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Universiti Kebangsaan Malaysia
2015
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| Online Access: | http://journalarticle.ukm.my/8990/1/17_Esra_Gokpinar.pdf |
| _version_ | 1796930890234855424 |
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| author | Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza |
| author_facet | Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza |
| author_sort | Gökpınar, Esra |
| collection | UKM |
| 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. |
| first_indexed | 2024-03-06T04:09:53Z |
| format | Article |
| id | ukm.eprints-8990 |
| institution | Universiti Kebangsaan Malaysia |
| language | English |
| last_indexed | 2024-03-06T04:09:53Z |
| publishDate | 2015 |
| publisher | Universiti Kebangsaan Malaysia |
| record_format | dspace |
| spelling | ukm.eprints-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 |
| spellingShingle | Gökpınar, Esra Khaniyev, Tahir Gamgam, Hamza Asymptotic properties of the straight line estimator for a renewal function |
| title | 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_short | Asymptotic properties of the straight line estimator for a renewal function |
| title_sort | asymptotic properties of the straight line estimator for a renewal function |
| url | http://journalarticle.ukm.my/8990/1/17_Esra_Gokpinar.pdf |
| work_keys_str_mv | AT gokpınaresra asymptoticpropertiesofthestraightlineestimatorforarenewalfunction AT khaniyevtahir asymptoticpropertiesofthestraightlineestimatorforarenewalfunction AT gamgamhamza asymptoticpropertiesofthestraightlineestimatorforarenewalfunction |