The correlation assumes that both variables are normally distributed and that the bivariate distribution is multivariate normal, which is not satisfied in our data.
Above, E p (x,y ) and E p (x ) p (y ) denote expectations taken under the assumptions that (X,Y) follow either a bivariate distribution (association) or that these variables are independently distributed.
These features are the same as those for copolymers (N = 2), which is conveniently represented by the Stockmayer bivariate distribution.
Based on available experimental evidence an explicit form of bivariate distribution is also constructed and its consequences are examined.
The Nataf distribution and copula models for characterizing the bivariate distribution of shear strength parameters are briefly introduced.
The Gaussian approximation of the composition distribution is a practical method to theoretically calculate the bivariate distribution formed in multicomponent polymerizations.
In a successive step, bivariate distribution of chain sizes and composition maps are derived from knowledge of the molar mass, weight and composition of the copolymer fractions.
The compositional distribution is obtained by summation of the sections of the bivariate distribution which belong to a narrow compositional range.
The theory of Markovian processes is used to investigate the bivariate distribution of chain length and composition in free-radical polymerization consisting of N types of monomer.
We conduct laboratory experiments and numerical simulations, and analyze field wave data to investigate the bivariate distribution of two fundamental characteristics of wave groupiness, group height and group length.
We develop a simple approach to finding the Fisher information matrix (FIM) for a single pair of order statistic and its concomitant, and Type II right, left, and doubly censored samples from an arbitrary bivariate distribution.
