### Abstract

Overdispersion often being a problem in modeling count data because the Poisson distribution that is often used to modeling count data cannot conquer the overdispersion data. Several distributions have been introduced to be used as an alternative to the Poisson distribution on conquering dispersion in data. However, that alternative distribution has higher complexity than Poisson distribution in the number of parameters used. Therefore, a new distribution with similar distribution to Poisson is offered, which is Lindley distribution. Lindley distribution is a continuous distribution, then it cannot be used to modeling count data. Hence, discretization on Lindley distribution should be done using a method that maintains the survival function of Lindley distribution. Result distribution from discretization on Lindley distribution has one parameter and can be used to modeling overdispersion data so that distribution is appropriate to be used as an alternative to Poisson distribution in modeling overdispersed count data. The result distribution of Lindley distribution discretization is commonly called Discrete Lindley distribution. In this paper, characteristics of Discrete Lindley distribution that are obtained are unimodal, right skew, high fluidity and overdispersion. Based on numerical simulation, another characeristic of parameter is also obtained from Discrete Lindley distribution that has a large bias and MSE when parameter value around e^{-1}.

Original language | English |
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Title of host publication | Proceedings of the 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 |

Editors | Terry Mart, Djoko Triyono, Tribidasari Anggraningrum Ivandini |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735420014 |

DOIs | |

Publication status | Published - 1 Jun 2020 |

Event | 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 - Depok, Indonesia Duration: 9 Jul 2019 → 10 Jul 2019 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 2242 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Conference

Conference | 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019 |
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Country | Indonesia |

City | Depok |

Period | 9/07/19 → 10/07/19 |

### Keywords

- Count data
- Discrete Lindley distribution
- Lindley distribution
- overdispersion
- Poisson distribution

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## Cite this

*Proceedings of the 5th International Symposium on Current Progress in Mathematics and Sciences, ISCPMS 2019*[030024] (AIP Conference Proceedings; Vol. 2242). American Institute of Physics Inc.. https://doi.org/10.1063/5.0007950