Relationship between Morisita’s model for estimating the environmental density and the generalized Eulerian numbers. (English) Zbl 0721.62110
Summary: The environmental density has been defined by M. Morisita [G. Patil et al. (eds.), Stat. Ecology, 379-401 (1971)] as the value of a habitat expressing its unfavorableness for settling of an individual which has a strong mutual-repulsive influence to other individuals in an environment. Morisita studied mutual repulsive behavior of ant lions (Glenuroids japanicus) and provided a recurrence relation without an explicit solution for the probability distribution of individuals settling in each of two habitats in terms of the environmental densities and the numbers of individuals introduced. Here the recurrence relation is explicitly solved; certain interesting properties of the distribution are discussed including its relation to the generalized Eulerian numbers and the estimation of the parameters.
MSC:
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
| 11B68 | Bernoulli and Euler numbers and polynomials |
Keywords:
attraction; maximum likelihood estimation; environmental density; mutual repulsive behavior; recurrence relation; generalized Eulerian numbersReferences:
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