A new discrete distrlbution, with applications to survival, dispersal and dispersion

A nonparametric method of estimation of the population size in capture-recapture experiments

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 ( L C -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.

Two Useful Discrete Distributions to Model Overdispersed Count Data

The methods to obtain discrete analogues of continuous distributions have been widely considered in recent years. In general, the discretization process provides probability mass functions that can be competitive with the traditional model used in the analysis of count data, the Poisson distribution. The discretization procedure also avoids the use of continuous distribution in the analysis of strictly discrete data. In this paper, we seek to introduce two discrete analogues for the Shanker distribution using the method of the infinite series and the method based on the survival function as alternatives to model overdispersed datasets. Despite the difference between discretization methods, the resulting distributions are interchangeable. However, the distribution generated by the method of infinite series method has simpler mathematical expressions for the shape, the generating functions and the central moments. The maximum likelihood theory is considered for estimation and asymptotic inference concerns. A simulation study is carried out in order to evaluate some frequentist properties of the developed methodology. The usefulness of the proposed models is evaluated using real datasets provided by the literature.

On a connection between the polylogarithm function and the Bass diffusion model

The purpose of this paper is to establish a connection between the polylogarithm function and a continuous probability distribution. We provide closed-form expressions in terms of the polylogarithm function for all the moments of a continuous random variable related to the Bass diffusion model, which was introduced by Bass and is widely used in marketing science. In addition, a new integral representation of the polylogarithm of order n is achieved from a probabilistic formulation.