The Geometric ArcTan distribution with applications to model demand for health services

ABSTRACT

In this paper , a new discrete two–parameter distribution α ∈ ℜ − {0} and 0 < θ < 1, the Geometric ArcTan (GAT) distribution is introduced. The geometric distribution is a limiting case of this model when α tends to zero. Similarly to the the latter distribution, this probabilistic family is unimodal but the mode can be located at zero or in other point of the support. Then, after deriving some of its more relevant properties , the issue of parameter investigation is investigated. Next, the GAT distribution is used to explain the demand for health services by means of a regression model. Numerical results show that this new model outperforms the negative binomial distribution.

KEYWORDS:

• Estimation
• Geometric Distribution
• Medical Care
• Negative Binomial Distribution
• Overdispersion
• Regression

MATHEMATICS SUBJECT CLASSIFICATION:

• 62E15
• 62F07

Acknowledgements

The authors would like to express their gratitude to two anonymous referees for their relevant and useful comments. The authors thank to the Ministerio de Economía y Competitividad (projects ECO2013–47092, EGD and ECO and ECO2016–76203-C2-1-P, JMS) for partial support of this work. (Ministerio de Economía y Competitividad, Spain).

Notes

1 This statistics was computed with the following grouping procedure: the outermost classes were consolidated to produce theoretical class sizes of 5 or larger. It is known that χ² follows a chi–squared distribution with n₀ − k − 1 degree of freedom, where n₀ is the number of classes considered in order to compute the value of χ².

Additional information

Funding

Emilio Gomez-Deniz [ECO2013-47092]; Jose M. Sarabia [ECO2013-48326-C2-2-P]; Enrique Calderin-Ojeda [ECO2013-47092].