AFFINITY BETWEEN CONTAGIOUS NAD POISSON DISTRIBUTIONS FOR PRATICAL SAMPLING PURPOSES.

Dilermando PERECIN1

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 + m2/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 m2/k; if m2/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.