In this case, the baseline of the denominator is defined μ on the basis of both. However, the latter index has serious shortcomings, which are illustrated in the following analysis. The four terms of the denominator can be represented geometrically, as shown in the Additional Information section. By explicitly adding the value of the covariant, the index ensures that if X and Y are negatively correlated, an index is equal to zero, as can be seen in Figure 3. However, if the denominator is inflated unnecessarily by this covariance, because the counter is smaller and smaller due to the negative sign before the covariance in equation (10). To solve this problem, we propose to define the index, which we simply call λ: the transformation of the Arcsinus function is justified by Watterson to allow linear convergence with the unit, while maintaining the original properties of the Mielke index8. The logic behind Mielke7`s original design of the index, based on all sorts of permutations between the elements in the two data sets, intuitively suggests how its denominator is actually the maximum possible value that the average sum of squares can reach. Because of the mathematical properties of these square deviations, it is possible to rewrite this index in an expression based on variances rather than permutations, which greatly simplifies the calculation. Unfortunately, we have not been able to generalize the (easily predictable) index structure to use with other deviation metrics, such as average absolute deviations.
However, the demonstration of how the inssystem can be disentangled from the systematic contribution to the agreement through self-destruction could be applied to any other type of metric. Figure 2 shows how the four metrics analyzed evolve in the generated datasets based on the imposed additive and multiplicative distortion and the initial correlation between X and Y. A first remark on the diagrams of columns (a) and (b) of Figure 2 is that there is an intersection of isolines for all metrics. Metrics are considered a correct decrease in compliance when there is increased systematic disruption for all types of correlations. Exceeding these iso-malfunction lines means that this assumption is violated. Abnormal behaviors can also be observed with moderate correlation values (e.g. .B. with r between 0.5 and 0.7). For them, and M, all lines intersect. This can be considered less uncomfortable, as the negative values of the indices could be used to evaluate the number of data sets corresponding to the size, although they do not correspond to the warning sign. However, this results in ambiguities in the interpretation of the index that are not desirable. A second point is that ji & Gallos AC is not negatively limited by zero as it was designed.
This happens even if no systematic disruption is added to the data (i.e. when and still with a fairly high positive correlation). These are conditions that can easily be expected for most recordings, which indicates how to avoid Ji & Gallos AC. Willmott6,20 suggested that its convergence indices could provide additional information by separating the effects due to the systematic components of the spreads. This idea can be indexed to anyone that is formulated with equation (3) by breaking down the gaps into their systematic and non-systematic components, and then defining as and defining new systematic and non-systematic indices. . . .