A note on the discrete normal distribution

  1. Ruiz Gómez, José María 1
  2. Navarro Camacho, Jorge Luis 1
  1. 1 Universidad de Murcia
    info

    Universidad de Murcia

    Murcia, España

    ROR https://ror.org/03p3aeb86

Journal:
Advances and Applications in Statistics

ISSN: 0972-3617

Year of publication: 2005

Volume: 5

Pages: 229-245

Type: Article

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Abstract

A. W. Kemp [J. Stat. Plann. Inference 63, No. 2, 223–229 (1997; Zbl 0902.62020)] studied a discrete analogue of the normal (Gauss) distribution extending work of R. Dasgupta [Theory Probab. Appl. 38, No. 3, 520–524 (1993) and Teor. Veroyatn. Primen. 38, No. 3, 661–666 (1993; Zbl 0807.60018)]. Kemp gives three characterizations of the discrete normal distribution including the characterization as a maximum entropy distribution (MED) in the integers for a given mean and a given variance. We reparametrize this model and obtain new properties, including two new characterizations. Moreover, we propose a generalization of this model and we give several tables to calculate the associated distribution function and to approach other discrete distributions.