Fitting the truncated negative binomial distribution to count data

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