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A recent method for estimating a lower bound of the population size in capture-recapture samples is studied. Specifically, some asymptotic properties, such as strong consistency and asymptotic normality, are provided. The introduced estimator is based on the empirical probability generating function (pgf) of the observed data, and it is consistent for count distributions having a log-convex pgf ( LC -class). This is a large family that includes mixed and compound Poisson distributions, and their independent sums and finite mixtures as well. The finite-sample performance of the lower bound estimator is assessed via simulation showing a better behavior than some close competitors. Several examples of application are also analyzed and discussed.

1. Zeros (i.e. events that do not happen) are the source of two common phenomena in count data: overdispersion and zero-inflation. Zeros have multiple origins in a dataset: false zeros occur due to errors in the experimental design or the observer; structural zeros are related to the ecological or evolutionary restrictions of the system under study; and random zeros are the result of the sampling variability. Identifying the type of zeros and their relation with overdispersion and/or zero inflation is key to select the most appropriate statistical model. 2. We first introduce the dispersion and zero inflation indeces and review the theory of the Zero-inflated (ZI) models and the use of the score tests to assess overdispersion and zero inflation over a model. Then, we present the following protocol to assist with the analysis of count data: Step 1) classify the zeros and minimize the presence of false zeros; Step 2) identify suitable covariates; Step 3) test the data for overdispersion and zero-inflation; and Step 4) choose the most adequate model based on the results of step 3 and use score tests to determine whether more complex models should be implemented. 3. We applied the recommended protocol on a real dataset on plant-herbivore interactions to evaluate the suitability of six different models (Poisson, NB and their zero-inflated versions –ZIP, ZINB–) in the light of overdispersion and zero inflation. Finally, we discuss the consequences of adjusting suboptimal models. 4. Our data was overdispersed and zero-inflated, and the ZINB was the model with the best fit, as predicted. Ignoring overdispersion and/or zero inflation during data analyses caused biased estimates of the statistical parameters and serious errors in the interpretation of the results. Our results are a clear example on how the conclusions of an ecological hypothesis can change depending on the model applied. Understanding of how zeros arise in count data, for example identifying the potential sources of structural zeros, is essential to select the best statistical design. A good model not only fits the data correctly but also takes into account the idiosyncrasies of the biological system under study.

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.

Within the field of cytogenetic biodosimetry, Poisson regression is the classical approach for modeling the number of chromosome aberrations as a function of radiation dose. However, it is common to find data that exhibit overdispersion. In practice, the assumption of equidispersion may be violated due to unobserved heterogeneity in the cell population, which will render the variance of observed aberration counts larger than their mean, and/or the frequency of zero counts greater than expected for the Poisson distribution. This phenomenon is observable for both full- and partial-body exposure, but more pronounced for the latter. In this work, different methodologies for analyzing cytogenetic chromosomal aberrations datasets are compared, with special focus on zero-inflated Poisson and zero-inflated negative binomial models. A score test for testing for zero inflation in Poisson regression models under the identity link is also developed.

We characterize all symmetric location models for which a linear combination of the median and the sample mean is an asymptotically efficient estimator of the location parameter. The resulting model can be understood as a symmetrized or double truncated normal distribution. A simple algorithm to estimate the parameters is given and an application is presented.

For Location and Scale models with Type I Censored Data the estimation of the parameters based on likelihood is analyzed. When the sample size is very small the usual procedures for inference based on the asymptotic distribution of the statistics do not function properly. We develop higher-order asymptotic methods and their performance is investigated by Monte Carlo experiments.

The authors give tests of fit for the hyperbolic distribution, based on the Cramer-von Mises statistic W2. They consider the general case with four parameters unknown, and some specific cases where one or two parameters are fixed. They give two examples using stock price data.