Modified binomial and Poisson distributions with applications in random mapping theory (Q1110209)

Random mapping theory gives rise to interesting discrete probability distributions. Here we focus on binomial- and Poisson-type distributions, useful for describing simple characteristics of random mappings. Properties of these distributions are discussed. For a particular random mapping suggested by the second author [Graphs and other combinatorial topics, Proc. 3rd Czech. Symp., Prague 1982, Teubner-Texte Math. 59 (1983; Zbl 0523.05057)], we consider inference problems for a key model parameter. Random mapping models have been proposed as models of social and biological diffusion phenomena. Therefore, it is important to develop statistical tools for testing and evaluating these models.