Bias-reduced maximum likelihood estimation of the zero-inflated Poisson distribution.

Jacob Schwartz, David E. Giles

Research output: Contribution to journalArticlepeer-review


We investigate the small-sample quality of the maximum likelihood estimators (MLE) of the parameters of a zero-inflated Poisson distribution (ZIP). The finite-sample bias of the MLE is determined toO(n−1) using an analytic bias-reduction methodology based on the work of Cox and Snell (1968) and Cordeiro and Klein (1994). Monte Carlo simulations show that the MLEs have very small percentage biases for this distribution, but the analytic bias-reduction methods essentially eliminate the bias without adversely affecting the mean-squared errors of the estimators. The analytic adjustment compares favorably with the parametric bootstrap bias-corrected estimator, in terms of bias reduction itself, as well as with respect to mean-squared error and Pitman’s nearness measure.
Original languageEnglish
Pages (from-to)465-478
Number of pages14
JournalCommunications in Statistics - Theory and Methods
Issue number2
StatePublished - 15 Jan 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2016 Taylor & Francis Group, LLC.


  • MAXIMUM likelihood statistics
  • ZERO-inflated probability distribution
  • BIAS correction (Topology)
  • MONTE Carlo method
  • PITMAN'S measure of closeness
  • POISSON distribution
  • 62F10
  • 62F40
  • 62N02
  • 62N05
  • Bias reduction
  • Finite sample properties
  • Maximum likelihood estimation
  • Zero-inflated Poisson distribution


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