Extensions of discrete triangular distributions and boundary bias in kernel estimation for discrete functions

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• 作者：Cé ; lestin C. Kokonendji ; Silvio S. Zocchi
• 关键词：Asymmetric discrete distribution ; Discrete associated kernel ; Finite support ; Limit distribution
• 刊名：Statistics and Probability Letters
• 出版年：2010
• 出版时间：1 November 2010-15 November 2010
• 年：2010
• 卷：80
• 期：21-22
• 页码：1655-1662
• 全文大小：355 K

文摘

Asymmetric discrete triangular distributions are introduced in order to extend the symmetric ones serving for discrete associated kernels in the nonparametric estimation for discrete functions. The extension from one to two orders around the mode provides a large family of discrete distributions having a finite support. Establishing a bridge between Dirac and discrete uniform distributions, some different shapes are also obtained and their properties are investigated. In particular, the mean and variance are pointed out. Applications to discrete kernel estimators are given with a solution to a boundary bias problem.