The extended Glivenko-Cantelli property for Kernel-Smoothed estimator of the cumulative distribution function in the length-biased sampling
| Autor: | Masoud Ajami, Raheleh Zamini, Seyed Mahdi Amir Jahanshahi |
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| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Journal of Mahani Mathematical Research, Vol 13, Iss 2, Pp 535-545 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2251-7952 2645-4505 |
| DOI: | 10.22103/jmmr.2024.22620.1546 |
| Popis: | Let $\{Y_i; i = 1,\ldots,n \}$ be a length-biased sample from a population with cumulative distribution function $F(\cdot)$. If the probability of an item selected in the sample is proportional to its length, then the distribution of the observed length is known as the length-biased distribution.We consider the kernel-type estimator $F_n^s(\cdot)$ of $F(\cdot)$. Under suitable conditions, the extended Glivenko-Cantelli theorem for $F_n^s(\cdot)$ is proved. |
| Databáze: | Directory of Open Access Journals |
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