|Fitting the truncated negative binomial distribution to count data. A comparison of estimators, with an application to groundfishesfrom the Mauritanian Exclusive Economic Zone |
(Article) Publié: Environmental And Ecological Statistics, vol. 23 p.359-385 (2016)
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A frequent issue in the study of species abundance consists in modeling empirical distributions of repeated counts by parametric probability distributions. In this setting, it is desirable that the chosen family of distributions is exible enough to take into account very diverse patterns, and that its parameters possess clear biological/ecological meanings. This is the case of the Negative Binomial distribution, chosen in this work for modeling counts of marine shes and invertebrates. This distribution depends on a vector (K, P) of parameters, and ranges from the Poisson distribution (when K → +∞) to Fisher's log-series, when K → 0. Besides, these parameters have biologi-cal/ecological interpretations detailed in the literature and reminded hereafter. We focus on the comparison of three estimators of K, P and the parameter α of Fisher's log-series, revisiting a nice paper of Rao (1971) about a three-parameter unstandardized variant of the Negative Binomial distribution. We investigate the coherency of values of the parameters resulting from these different estimators, with both real count data collected in the Mauritanian Exclusive Economic Zone during the period 1987-2010 and realistics simulations of theses data. In the rst case, we rst built homogeneous lists of counts (replicates), by gathering observations of each species with respect to typical environments obtained by clustering the sampled stations. The best estimation of (K, P) was generally obtained by Penalized Minimum Hellinger Distance Estimation. Interestingly, the parameters of most of the correctly sampled species seem compatible with a classical birth-and-dead model of population growth with immigration of Kendall (1948).