### Abstract

Traffic accident data is usually over dispersed and has extra zeros. Zero-inflated negative binomial distribution (ZINB) has often been used to fit this type of data. A simulation study has been conducted to investigate the performance of the estimators of the ZINB with different proportions of zeros. It is found that the commonly used Maximum Likelihood Estimator (MLE) produce inaccurate estimates of the parameters for data with low proportion of zeros. Hence, the aim of this study is to propose an alternative method to fit the zero-inflated negative binomial distribution. The alternative method consists of two phases: a grid search and conditional maximum likelihood estimator (GCMLE). The empirical results indicate that this method produces better results than MLE in terms of smaller bias for dispersed data with a moderate proportion of zeros.

Original language | English |
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Pages (from-to) | 2461-2467 |

Number of pages | 7 |

Journal | Global Journal of Pure and Applied Mathematics |

Volume | 11 |

Issue number | 4 |

Publication status | Published - 2015 |

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### Keywords

- Count data
- Negative binomial
- Traffic accident
- Zero-inflated

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**An alternative method for fitting a zero inflated negative binomial distribution.** / Zamzuri, Zamira Hasanah.

Research output: Contribution to journal › Article

*Global Journal of Pure and Applied Mathematics*, vol. 11, no. 4, pp. 2461-2467.

}

TY - JOUR

T1 - An alternative method for fitting a zero inflated negative binomial distribution

AU - Zamzuri, Zamira Hasanah

PY - 2015

Y1 - 2015

N2 - Traffic accident data is usually over dispersed and has extra zeros. Zero-inflated negative binomial distribution (ZINB) has often been used to fit this type of data. A simulation study has been conducted to investigate the performance of the estimators of the ZINB with different proportions of zeros. It is found that the commonly used Maximum Likelihood Estimator (MLE) produce inaccurate estimates of the parameters for data with low proportion of zeros. Hence, the aim of this study is to propose an alternative method to fit the zero-inflated negative binomial distribution. The alternative method consists of two phases: a grid search and conditional maximum likelihood estimator (GCMLE). The empirical results indicate that this method produces better results than MLE in terms of smaller bias for dispersed data with a moderate proportion of zeros.

AB - Traffic accident data is usually over dispersed and has extra zeros. Zero-inflated negative binomial distribution (ZINB) has often been used to fit this type of data. A simulation study has been conducted to investigate the performance of the estimators of the ZINB with different proportions of zeros. It is found that the commonly used Maximum Likelihood Estimator (MLE) produce inaccurate estimates of the parameters for data with low proportion of zeros. Hence, the aim of this study is to propose an alternative method to fit the zero-inflated negative binomial distribution. The alternative method consists of two phases: a grid search and conditional maximum likelihood estimator (GCMLE). The empirical results indicate that this method produces better results than MLE in terms of smaller bias for dispersed data with a moderate proportion of zeros.

KW - Count data

KW - Negative binomial

KW - Traffic accident

KW - Zero-inflated

UR - http://www.scopus.com/inward/record.url?scp=84944725938&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944725938&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84944725938

VL - 11

SP - 2461

EP - 2467

JO - Global Journal of Pure and Applied Mathematics

JF - Global Journal of Pure and Applied Mathematics

SN - 0973-1768

IS - 4

ER -