University of Tehran Journal of Sciences, Islamic Republic of Iran 1016-1104 24 1 2013 03 01 Some Asymptotic Results of Kernel Density Estimator in Length-Biased Sampling 55 62 31923 EN M. Ajami Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran V. Fakoor Department of Statistics, School of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Islamic Republic of Iran S. Jomhoori Department of Statistics, Faculty of Sciences, University of Birjand, Birjand, Islamic Republic of Iran Journal Article 2012 09 10 In this paper, we prove the strong uniform consistency and asymptotic normality of the kernel density estimator proposed by Jones [12] for length-biased data.The approach is based on the invariance principle for the empirical processes proved by Horváth [10]. All simulations are drawn for different cases to demonstrate both, consistency and asymptotic normality and the method is illustrated by real automobile brake pads data. https://jsciences.ut.ac.ir/article_31923_6ffab824d9a053a13108a5d09cad8ebb.pdf