Skewness parameter

An asymmetry or skewness parameter, f, ranging between 0 and 1 may be defined as... 

Uj+i ordinate of (j + l)th reactant input in synthesis plan AE atom economy fi asymmetry (skewness) parameter... 

An edditional measure of the PSD is the skewness parameter s. defined by Garden (1968b) as the exponent of the radius such that the PSD expressed in tbe size parameter (radius) is most nearly Gaussian. 

The column-vector 7 contains the skewing parameter ja- This parameter determines how much the calculation of a variable A i) is delayed relatively to the scheduling determined by t. This permits dealing with potentially complex processing elements that contain, for instance, internal pipelining. 

The ultimate goal of the overall space-time mapping step is to find a transformation matrix f and a set of skewing parameters 7a that result in an optimized... 

In this case, it was possible to linearize the multidimensional timing in a simple way, and only internal pipelining is necessary within the PE with the appropriate skewing parameters 7a [19]. 

When analyzing copolymers or polymer blends in LAC mode, the retention time is indicative of the average chemical composition and the peak width is a measure of the CCD. The retention axis has to be calibrated either by standards with known chemical composition or multiple detector combinations can be employed to measure the local chemical composition. The average chemical composition of a copolymer can be easily described by the moments of the CCD. The average composition, G, the width, dG, and the skew, S, of the CCD can easily be calculated. The value of the skew parameter is zero, if the composition distribution is symmetrical. 

The Erlang number /leriang. nd the variances O (t ) and 0 (t) are single parameter characterizations of RTD curves. The skewness y (t), and higher moments can be used to represent RTD curves more closely if the data are accurate enough. 

Data that is not evenly distributed is better represented by a skewed distribution such as the Lognormal or Weibull distribution. The empirically based Weibull distribution is frequently used to model engineering distributions because it is flexible (Rice, 1997). For example, the Weibull distribution can be used to replace the Normal distribution. Like the Lognormal, the 2-parameter Weibull distribution also has a zero threshold. But with increasing numbers of parameters, statistical models are more flexible as to the distributions that they may represent, and so the 3-parameter Weibull, which includes a minimum expected value, is very adaptable in modelling many types of data. A 3-parameter Lognormal is also available as discussed in Bury (1999). 

To examine the effects of height distribution on mixed lubrication, rough surfaces with the same exponential autocorrelation function but different combinations of skewness and kurtosis have been generated, following the procedure described in the previous section. Simulations were performed for the point contact problem with geometric parameters of... 

It would be of obvious interest to have a theoretically underpinned function that describes the observed frequency distribution shown in Fig. 1.9. A number of such distributions (symmetrical or skewed) are described in the statistical literature in full mathematical detail apart from the normal- and the f-distributions, none is used in analytical chemistry except under very special circumstances, e.g. the Poisson and the binomial distributions. Instrumental methods of analysis that have Powjon-distributed noise are optical and mass spectroscopy, for instance. For an introduction to parameter estimation under conditions of linked mean and variance, see Ref. 41. 

If the right side of this equation is plotted versus dimensionless time for various values of the group Q)JuL (the reciprocal Peclet number), the types of curves shown in Figure 11.8 are obtained. The skewness of the curve increases with 3) JuL and, for small values of this parameter, the shape approaches that of a normal error curve. In physical terms this implies that when 3JuL is small, the shape of the axial concentration profile does not change... 

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