Sentence examples for by the variance function from inspiring English sources

Given p≥1 and (lambda in mathbf {R}_^{1}), the one-parameter class {Tw p,μ∈Ω p } comprises a natural exponential family (or NEF) of non-negative distributions which is characterized by the variance function of a power type.

By using the variance function, the mean value and the lower end of the range i.e., the first 1 per cent of the mainlobe width distribution, can be predicted with reasonable accuracy.

For logistic and Poisson models, as examples, we incorporate the variance function prescribed by a superior model similar to a generalized linear mixed model to address overdispersion, and adopt a parameterized generalized family of link functions to deal with the problem of link misspecification.

The NIC of the OSTAR-GARCH model determined by the conditional variance function in (4) and the tumbler transition function in (3) is represented as the black line in Fig. 2.

Modelling the residual variance at the cluster level by using variance function (varIdent) improved the model performance as measured by the AIC.

Results based on the LMM illustrate that incorporating the cluster structure by using variance function in the model selection process can result in a model with better fit, as supported by the likelihood ratio test.

We find that there are two kinds of design determined by the model parameters and the error variance function: "interior" designs, and "boundary" designs that depend also on the design range.

The first of them employs the above variance function (mathbf {V}_{{mathcal Z}_{p}}(cdot)) given by (37).

When xt is strictly stationary on a strongly mixing base (hereby allowing for ARCH effects) the nonparametric variance function estimator by Fan and Yao [1998. Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85, 645 660] can be applied and seems very promising.

Chi-square statistic with the Gehrels variance function.

Results could be readily extrapolated to a three-dimensional medium by modifying the corresponding variance functions.