In the case of a single trait, the genetic selection gradient (βA) is defined as the genetic covariance between the trait and relative fitness (σa,w) divided by the additive genetic variance in the trait (σa) [ 27]: (Eq.1) β A = σ a, ω σ a 2 The selection analysis can be easily extended to the multivariate case, to account for selection on correlated characters [ 28].
Population balance modeling is a widely used approach to describe, crystallization processes, taking into accountnot only the primary phenomena like nucleation and growth, as well asparticle agglomeration and breakage which can be extended to multivariate cases where more internal coordinates i.e. particle properties can be used.
In the multivariate case, In order to obtain equivariant estimates, it is of advantage to estimate location and dispersion simultaneously [28].
In multivariate cases, cokriging has been the traditional approach to solve the problem.
At very high (95%) confidence, no signals are detected for RX1D, while for the RX5D and multivariate cases only the anthropogenic (ANT) signal is detected, though the fingerprints are in general found to be noisy.
The results show that for both univariate and multivariate cases, the nonparametric Gaussian kernel provides the best estimate.
We provide the interested reader with further properties of these stochastic orders in both the univariate and the multivariate cases.
Given historical data for continuous univariate or multivariate random variables (uncertain parameters in an optimization model), the inverse cumulative distribution function (quantile function) and the joint cumulative distribution function are estimated for the univariate and multivariate cases, respectively.
hOther multivariate cases include those by Mullahy and Robert ([2010]), Mullahy ([2004], [2010]) and Koch ([2010]), as well as studies from other thematic areas, e.g., agricultural (Mu et al., [2013]) or transportation research (Ye and Pendyala [2005]).
