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February 2020 On the Nielsen distribution
Fredy Castellares, Artur J. Lemonte, Marcos A. C. Santos
Braz. J. Probab. Stat. 34(1): 90-111 (February 2020). DOI: 10.1214/18-BJPS414

Abstract

We introduce a two-parameter discrete distribution that may have a zero vertex and can be useful for modeling overdispersion. The discrete Nielsen distribution generalizes the Fisher logarithmic (i.e., logarithmic series) and Stirling type I distributions in the sense that both can be considered displacements of the Nielsen distribution. We provide a comprehensive account of the structural properties of the new discrete distribution. We also show that the Nielsen distribution is infinitely divisible. We discuss maximum likelihood estimation of the model parameters and provide a simple method to find them numerically. The usefulness of the proposed distribution is illustrated by means of three real data sets to prove its versatility in practical applications.

Citation

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Fredy Castellares. Artur J. Lemonte. Marcos A. C. Santos. "On the Nielsen distribution." Braz. J. Probab. Stat. 34 (1) 90 - 111, February 2020. https://doi.org/10.1214/18-BJPS414

Information

Received: 1 December 2017; Accepted: 1 August 2018; Published: February 2020
First available in Project Euclid: 3 February 2020

zbMATH: 07200393
MathSciNet: MR4058972
Digital Object Identifier: 10.1214/18-BJPS414

Rights: Copyright © 2020 Brazilian Statistical Association

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Vol.34 • No. 1 • February 2020
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