Red flesh watermelon is one of the main food sources with lycopene as the most abundant carotenoid and has been associated with a lowered risk of prostate cancer. In order to assess health benefits of Portuguese watermelon, five acessions from the Portuguese Bank of Germplasm were were chosen for antioxidant quantification and total solids content. Two of the acessions were further characterized for lycopene co...
O sector energético assume particular relevo no contexto nacional, quer pelas suas repercussões no aparelho produtivo, quer pelas consequências ao nível do emprego, do abastecimento interno, das relações com o exterior e do ambiente. Devido à forte dependência energética do exterior, e ao peso do consumo dos combustíveis fósseis no consumo de energia primária, o país enfrenta grandes desafios ao nível das polít...
We find conditions under which the sequence of empirical means of associated random variables, , satisfies the large deviation principle. ; http://www.sciencedirect.com/science/article/B6V1D-4R0CJY8-6/1/c39727bbf213146fdbba98b7b50fd575
Abstract Let X n , n = 1, be a strictly stationary associated sequence of random variables, with common continuous distribution function F. Using histogram type estimators we consider the estimation of the two-dimensional distribution function of (X 1,X k+1) as well as the estimation of the covariance function of the limit empirical process induced by the sequence X n , n = 1. Assuming a convenient decrease...
We prove convergence rates for the Strong Laws of Large Numbers (SLLN) for associated variables which are arbitrarily close to the optimal rates for independent variables. A rst approach is based on exponential inequalities, a usual tool for this kind of problems. Following the optimization e orts of several authors, we improve the rates derived from exponential inequalities to log2 n n1=2 . A more recent appr...
Let Xn, n=1, be an associated and strictly stationary sequence of random variables, having marginal distribution function F. The limit in distribution of the empirical process, when it exists, is a centred Gaussian process with covariance function depending on terms of the form ?k(s, t)=P(X1 s, Xk+1 t)-F(s)F(t). We prove the almost sure consistency for the histogram to estimate each ?k and also to estimate ...
Exponential inequalities for associated variables are derived under an assumption milder than the absolute continuity of joint distributions of the sample variables. This inequality is used to prove convergence rates for the kernel estimator for the density which are just slightly slower than the optimal rates known form independent samples. ; Centro de Matemática da Universidade de Coimbra
The empirical process induced by a sequence of associated random variables has for limit in distribution a centered Gaussian process with covariance function defined by an infinite sum of terms of the form .k(s, t) = P(X1 . s,Xk+1 . t). F(s)F(t). We study the estimation of such series using the histogram estimator. Under a convenient decrease rate on the covariance structure of the variables we prove the strong...
The estimation of density based on positive dependent samples has been studied recently with consistency and asymptotic normality results being obtained. In what concerns the characterization on decrease rates the results have been scarce. The article proves an exponential decrease rate for the kernel estimator of the density with an uniform version, over compact sets. The conditions assumed impose convenient d...
Tendo como objectivo despertar o interesse dos alunos pelo cálculo de probabilidades, as autoras desta sessão de trabalho, pegaram num tema bem conhecido de todos, o jogo do Totoloto, e fizeram dele um tema de trabalho em probabilidades para cerca de uma hora. As autoras começaram por despertar nos alunos a curiosidade por saber quais são as chances de ganhar o 1º, 2º, 3º, 4º e 5º prémio, no...
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