An alternative method for fitting a zero inflated negative binomial distribution

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3 Citations (Scopus)

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 languageEnglish
Pages (from-to)2461-2467
Number of pages7
JournalGlobal Journal of Pure and Applied Mathematics
Volume11
Issue number4
Publication statusPublished - 2015

Fingerprint

Negative binomial distribution
Maximum likelihood
Alternatives
Zero
Maximum Likelihood Estimator
Highway accidents
Proportion
Conditional Maximum Likelihood
Inaccurate
Accidents
Traffic
Simulation Study
Grid
Estimator
Estimate

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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title = "An alternative method for fitting a zero inflated negative binomial distribution",
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.",
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T1 - An alternative method for fitting a zero inflated negative binomial distribution

AU - Zamzuri, Zamira Hasanah

PY - 2015

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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.

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