AFFINITY BETWEEN CONTAGIOUS NAD POISSON
DISTRIBUTIONS FOR PRATICAL SAMPLING PURPOSES.

Dilermando PERECIN^{1}

José Carlos BARBOSA[1]

§ ABSTRACT: Contagious distributions
are very common in agronomic research, as insect countings or weed distribution
per area. They are characterized for having a variance larger than the mean. In
general, are difficult to work with them and the parameters are different in
each practical situation. The most used one, is the negative binomial
distribution (s ^{2} =
m + m^{2}/k, were, m = mean, k = dispersion parameter). When the mean
tends to zero or k tends to infinity, the variance tends to the expected
variance obtained by Poisson distribution. In this article, theoretical and
simulated data for Poisson distribution with means 0.5, 1.0, 1.5, 2.0 e 5.0,
and negative binomial distribution with equals means, and overdispersion in the
variances of de 10, 20, 50, 100, 200 e 400%were studied. In the case of the
negative binomial distribution, the overdispersion is m^{2}/k; if m^{2}/k<0.5
m (50% of the mean), then we have the mean smaller that k/2. In these
conditions, the lack of affinity will be smaller than 20% , and the Poisson
distribution can be used. This can be obtained in the practice using an
adequate plot size, where the counting mean will be smaller than k/2, or the
ratio variance/mean being smaller than 1.5.

§ KEYWORDS: Contagious distributions;
sampling; overdispersion; relation variance/mean.

[1] Departamento de Ciências Exatas da Faculdade de Ciências Agrárias e Veterinárias - UNESP- 14870-000 - Jaboticabal - SP .Bolsista do CNPq.