Proposta de uma distribuição bimodal sem mistura: uma aplicação em dados de teor de sólidos solúveis de cana-de-açúcar - Medeiros, Marcelo Lemos de (2009)
In the scientifics papers in various areas of knowledge, when they face modeling problems with bimodal characteristics in random variables continuous, usually opt to use mixed distributions or mixture of distributions. These procedures are generally in the adjustment of two distinct or not models with weighting factors p and 1-p (0 < p < 1). This is done for each model, in its range of random variable domain studied so that the transceivers are combined into the real domain. In General, the usual distribution mixtures presents many parameters, and therefore the solution of the equations system that make up these parameters is not analytical and requires use of unusual iterative algorithms for professionals. This paper aimed to build a model of bimodal probability density with single mathematical law and explicit estimators for their parameters. It was obtained a model which belongs to the exponential family with four parameters: two of the location, one of shape and one of scale. The maximum likelihood estimators of positional parameters were obtained by simple iteration and others presented explicit forms. The method of moments did not allow the estimation of position parameters. A sample of 620 observations of soluble solids content (in DEGREES Brix) sugar cane harvested in 2007 a crop in a sugar factor and distillery in Araraquara city (São Paulo State - Brazil) which has presented bimodal characteristics, was used to the application of the model proposed. The results obtained have enabled explain satisfactorily the phenomenon in study. It´s suggested the use of bimodal density model proposed as an alternative to the models proposed of mixed distributions to work the random variables with bimodal behavior and to contribute to popularize science areas modeling with less affinity for advanced computing statistics.