The target measure µ is the distribution of a random vector in a box B, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure µ. A 'coupling from the past'construction of the Gibbs sampler is used to show ergodicity of the dynamics and to perfectly simulate µ. An algorithm to sample vectors with multinormal distribution truncated to B is then implemented.
The target measure µ is the distribution of a random vector in a box B, a Cartesian product of bounded intervals. The Gibbs sampler is a Markov chain with invariant measure µ. A "coupling from the past" construction of the Gibbs sampler is used to show ergodicity of the dynamics and to perfectly simulate µ. An algorithm to sample vectors with multinormal distribution truncated to B is then implemented.
In the financial markets, there is a well established portfolio optimization model called generalized mean-variance model (or generalized Markowitz model). This model considers that a typical investor, while expecting returns to be high, also expects returns to be as certain as possible. In this paper we introduce a new media optimization system based on the mean-variance model, a novel approach in media planning. After presenting the model in its full generality, we discuss possible advantages of the mean-variance paradigm, such as its flexibility in modeling the optimization problem, its ability of dealing with many media performance indices -satisfying most of the media plan needs -and, most important, the property of diversifying the media portfolios in a natural way, without the need to set up ad hoc constraints to enforce diversification.Keywords: media planning; mean-variance optimization; parametric quadratic programming. ResumoNo mercado financeiro, existem modelos de otimização de portfólios já bem estabelecidos, denominados modelos de média-variância generalizados, ou modelos de Markowitz generalizados. Este modelo considera que um investidor típico, enquanto espera altos retornos, espera também que estes retornos sejam tão certos quanto possível. Neste artigo introduzimos um novo sistema otimizador de mídia baseado no modelo de média-variância, uma abordagem inovadora na área de planejamento de mídia. Após apresentar o modelo em sua máxima generalidade, discutimos possíveis vantagens do paradigma de média-variância, como sua flexibilidade na modelagem do problema de otimização, sua habilidade de lidar com vários índices de performance -satisfazendo a maioria dos requisitos de planejamento -e, o mais importante, a propriedade de diversificar os portfólios de mídia de uma forma natural, sem a necessidade de estipular restrições ad hoc para forçar a diversificação.Palavras-chave: planejamento de mídia; otimização de média-variância; programação quadrática paramétrica.
The constant c 4 [n] is commonly used in the construction of control charts and the estimation of process capability indices, where n denotes the sample size. Assuming the Normal distribution the unbiased estimator of the population standard deviation is obtained by dividing the sample standard deviation by the constant c 4 [n]. An alternative expression for c 4 [n] is proposed, and the mathematical induction technique is used to prove its validity. Some desirable properties are described. First, the suggested expression provides the exact value of c 4 [n]. Second, it is not a recursive formula in the sense it does not depend on the previous sample size. Finally, the value of c 4 [n] can be directly computed for large sample sizes. Such properties suggest that the proposed expression may be a convenient solution in computer programming, and it has direct applications in statistical quality control.
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