A survey of a hurdle model for heavy-tailed data based on the generalized lambda distribution

Abstract

We present a literature review on the current state of Generalized Lambda Distribution (GλD) research and propose a highly flexible GλD hurdle model for heavy tailed data with excessive zeros. We apply the developed models to a dataset consisting of yearly healthcare expenses, a typical example of heavy-tailed data with excessive zeros. The fitted GλDs are compared with models based on the Generalised Pareto Distribution and it is established that the GλD performs the best.

Keywords:

• Generalized Lambda Distribution
• Generalized Pareto Distribution
• hurdle models
• two-way models

Acknowledgements

We would like to thank Sabesprev who kindly provided the dataset used in this paper.

Notes

1 The algorithm in Su (2007b) has five steps, that we reduced to four, without loss of content.

2 The same conventions apply to the RS GλD.

3 This is also the case for the RS GλD.

4 $1$ is the indicator function.

5 The number 1000 is arbitrary. It could be sampled more or less coefficients.

6 W and Z are random vectors which may share some variables or be equal.

7 Brazilian currency.