Statistical Modelling 3 (2003), 305–322

Point and interval estimation of the population size using the truncated Poisson regression model

Peter G.M. van der Heijden
Department of Methodology and Statistics,
Utrecht University,
P.O. Box 80.140,
NL-3508 TC   Utrecht,
The Netherlands.

Rami Bustami, and Maarten J.L.F. Cruyff
Department of Methodology and Statistics,
Utrecht University,
Utrecht, The Netherlands.

Godfried Engbersen
Faculty of Social Sciences,
Erasmus Univerity Rotterdam,
Rotterdam, The Netherlands.

Hans C. van Houwelingen
Department of Medical Statistics,
Leiden University Medical Center,
Leiden, The Netherlands.


A method is presented to derive point and interval estimates of the total number of individuals in a heterogenous Poisson population. The method is based on the Horvitz-Thompson approach. The zero-truncated Poisson regression model is fitted and results are used to obtain point and interval estimates for the total number of individuals in the population. The method is assessed by performing a simulation experiment computing coverage probabilities of Horvitz-Thompson confidence intervals for cases with different sample sizes and Poisson parameters. We illustrate our method using capture-recapture data from the police registration system providing information on illegal immigrants in four large cities in the Netherlands.


Capture-recapture; Horvitz-Thompson confidence interval; parametric bootstrap; population size estimation; truncated Poisson model.


Data and GAUSS code in zipped archive