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Ajami, Masoud, Zamini, Raheleh, Amir Jahanshahi, Seyed Mahdi. (1403). The extended Glivenko-Cantelli property for Kernel-Smoothed estimator of the cumulative distribution function in the length-biased sampling. , 13(2), 535-545. doi: 10.22103/jmmr.2024.22620.1546
Masoud Ajami; Raheleh Zamini; Seyed Mahdi Amir Jahanshahi. "The extended Glivenko-Cantelli property for Kernel-Smoothed estimator of the cumulative distribution function in the length-biased sampling". , 13, 2, 1403, 535-545. doi: 10.22103/jmmr.2024.22620.1546
Ajami, Masoud, Zamini, Raheleh, Amir Jahanshahi, Seyed Mahdi. (1403). 'The extended Glivenko-Cantelli property for Kernel-Smoothed estimator of the cumulative distribution function in the length-biased sampling', , 13(2), pp. 535-545. doi: 10.22103/jmmr.2024.22620.1546
Ajami, Masoud, Zamini, Raheleh, Amir Jahanshahi, Seyed Mahdi. The extended Glivenko-Cantelli property for Kernel-Smoothed estimator of the cumulative distribution function in the length-biased sampling. , 1403; 13(2): 535-545. doi: 10.22103/jmmr.2024.22620.1546

The extended Glivenko-Cantelli property for Kernel-Smoothed estimator of the cumulative distribution function in the length-biased sampling

Journal of Mahani Mathematical Research
دوره 13، شماره 2 - شماره پیاپی 27، آبان 2024، صفحه 535-545    اصل مقاله (515.65 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22103/jmmr.2024.22620.1546
نویسندگان
Masoud Ajami* 1؛ Raheleh Zamini2؛ Seyed Mahdi Amir Jahanshahi3
1Department of Statistics, Faculty of Mathematical Sciences, Vali-e-Asr University of Rafsanjan, Rafsanjan, Iran
2Department of Mathematics, Faculty of Mathematical Sciences and Computer, Kharazmi University, Tehran, Iran
3Department of Statistics, University of Sistan and Baluchestan, Zahedan
چکیده
‎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.
کلیدواژه‌ها
Extended Glivenko-Cantelli theorem؛ Smoothed estimator؛ Strong consistency
مراجع
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