Lucas Monteiro Chaves

Ajuste de modelos de platô de resposta via regressão isotônica

Within the nutritional context, the supplementation of microminerals in bird food is often made in quantities exceeding those required in the attempt to ensure the proper performance of the animals. The experiments of type dosage x response are very common in the determination of levels of nutrients in optimal food balance and include the use of regression models to achieve this objective. Nevertheless, the regression analysis routine, generally, uses a priori information about a possible relationship between the response variable. The isotonic regression is a method of estimation by least squares that generates estimates which preserves data ordering. In the theory of isotonic regression this information is essential and it is expected to increase fitting efficiency. The objective of this work was to use an isotonic regression methodology, as an alternative way of analyzing data of Zn deposition in tibia of male birds of Hubbard lineage. We considered the models of plateau response of polynomial quadratic and linear exponential forms. In addition to these models, we also proposed the fitting of a logarithmic model to the data and the efficiency of the methodology was evaluated by Monte Carlo simulations, considering different scenarios for the parametric values. The isotonization of the data yielded an improvement in all the fitting quality parameters evaluated. Among the models used, the logarithmic presented estimates of the parameters more consistent with the values reported in literature.

An Intuitive Geometric Approach to the Gauss Markov Theorem

ABSTRACT Algebraic proofs of Gauss–Markov theorem are very disappointing from an intuitive point of view. An alternative is to use geometry that emphasizes the essential statistical ideas behind the result. This article presents a truly geometrical intuitive approach to the theorem, based only in simple geometrical concepts, like linear subspaces and orthogonal projections.

Sums, Products and Ratios for Crovelli’s Bivariate Gamma Distribution

Bivariate gamma distributions have been used successfully on modeling hydrological processes. In this work, supposing that X and Y follow the Crovelli’s bivariate gamma model, we deduce the exact distributions of the functions U = X + Y, P = XY and Q = X/(X + Y), as well as their respective moments. Those functions are important hidrological variables. A MAPLE code to compute the quantiles is provided. An application of the results is provided to rainfall data from Passo Fundo.

Combinações de variáveis aleatórias beta tipo II aplicadas em modelagem hidrológica

The distributions of products and ratios of random variables are used in various fields of applied science and they have been intensively studied by several researchers. In this work they are deducted the exact distributions of X Y , X /Y and X /(X +Y ) when X and Y are independent beta type II random variables. The results found are applied to real data analysis of rainfall occurred in cities in the state of Sergipe.