Sentence examples for For some coefficients from inspiring English sources

For some coefficients, there exists a systematic bias (see, for instance, the positive trend taken by the average (dot {h}_{2}^{1}) forecast) : even though the observed series usually lies within the ensemble of forecast realizations, it sometimes lies in an area of lower probability, as measured by the pdf of the forecast.

The a posteriori errors we obtain exclude the occurrence of large variations for some coefficients at particular epochs (see the (tilde {h}_{n}^{0}), (tilde {h}_{1}^{1}), or (tilde {h}_{3}^{1}) coefficients in the early 1930s, a period of relatively weak solar activity).

The major interest of LASSO is that it allows a variable selection: the constraint induces nullity for some coefficients β j.

We contend that this approach is inconsistent with theory: the signal for some coefficients is included in the noise of others.

Note this generic form may have zero estimates for some coefficients (e.g., β ^ 2 = β ^ 5 = ⋯ = β ^ q = 0 ); hence an ITR can be equivalently constructed from the final estimated nonzero coefficients and the corresponding covariates.

While two-term polynomial fittings can almost exactly reproduce interaction coefficients at various temperatures, linear fittings for some interaction coefficients can also reproduce interaction coefficients at various temperatures within uncertainty of 2σ as exemplified by the case for ε(Ca2+, Cl-) at various temperatures (Figure 2).

For the case that some coefficients are transcendental meromorphic functions, the following two results were proved by Chaing and Feng [8] and Laine and Yang [16], respectively.

For some interaction coefficients, especially those involving complexes, because experimental data on mean activity coefficient are lacking, they are tested against equilibrium quotients (see below).

Although both linear and two-term polynomial expressions are given for some interaction coefficients, it is recommended to use two-term polynomial expressions for interpolations.

Linear relations for some interaction coefficients might be used for extrapolations over a limited range of temperatures beyond the temperatures at which they are evaluated (say, over a limited range of ~25°C).

In particular the GARCH model of order ((p,q)), indicated by ((operatorname{GARCH}(p,q))), defines the residual (epsilon_{t}) appearing in equation (1) as follows begin{aligned} &h_{t} = epsilon_{t} sigma_{t}, &sigma^{2}_{t} = alpha_{0} + sum _{k=1}^{q} alpha_{k} h_{t-k}^{2} + sum_{k=1}^{p} beta_{k}^{2} sigma^{2}_{t-k}, end{aligned} for some positive coefficients (alpha_{k}, beta_{k} geq0).