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

Célestin C. Kokonendji (1) , Silvio S. Zocchi (2)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 ESALQ - Escola Superior de Agricultura "Luiz de Queiroz"

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 solution to a boundary bias problem.

Mots clés: primary; secondary; Asymmetric discrete distribution; Discrete associated-kernel; Finite support; Limit distribution

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Célestin C. Kokonendji, Silvio S. Zocchi. Extensions of discrete triangular distribution and boundary bias in kernel estimation for discrete functions. Statistics and Probability Letters, 2010, 80 (21-22), pp.1655. ⟨10.1016/j.spl.2010.07.008⟩. ⟨hal-00671841⟩