Non‐parametric Estimation of the Number of Zeros in Truncated Count Distributions. (8th August 2017)

• Record Type: Journal Article
• Authors: Puig, Pedro; Kokonendji, Célestin C.
• Is Part Of: Scandinavian journal of statistics. Volume 45:Number 2(2018:Jun.)
• Page Start: 347
• Page End: 365
• Publication Date: 2017-08-08
• Subjects: capture‐recapture -- Chao's estimator -- population size -- Turing's estimator; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12293
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: We present some lower bounds for the probability of zero for the class of count distributions having a log‐convex probability generating function, which includes compound and mixed‐Poisson distributions. These lower bounds allow the construction of new non‐parametric estimators of the number of unobserved zeros, which are useful for capture‐recapture models, or in areas like epidemiology and literary style analysis. Some of these bounds also lead to the well‐known Chao's and Turing's estimators. Several examples of application are analysed and discussed.