Zero inflated Waring distribution

Abstract

Zero inflated distributions are used in a wide variety of phenomena, particularly when the response variable exhibits an excessive number of zeros. These phenomena can lead to an overdispersion in the data and the reduction of its mean. In this paper, we aim to address this issue by introducing the zero inflated Waring distribution (ZIW). The latter is regarded to fit the data more adequately in cases where the Waring distribution fails to accurately describe data behavior, especially when these contain a high frequency of observed zeros. Therefore, we propose a more flexible distribution than those found in the literature to address the presence of large tails to the right. This distribution encompasses both the overdispersion generated by the excess of zeros, and that generated by the Waring distribution. The estimation of parameters is calculated by using the maximum likelihood method. Monte Carlo simulation results are provided. Finally, a practical application with real data extracted from the literature is presented.

Keywords:

• Count data
• Maximum likelihood estimate
• Overdispersion
• Waring distribution
• Zero inflated distribution

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The authors acknowledgments the partial support from Projects VRID 215.014.025-1IN, Universidad de Concepción, Chile.