with covariance matrix V (bOLS) = σ (XX) Let us, however, assume more generally that ε ∼ Nn(0,Σ), where the error-covariance matrix Σ is symmetric and positive-definite. Different diagonal entries in Σ correspond to non-constant error variances, while nonzero off-diagonal entries correspond to correlated errors. Suppose, for the time-being, that Σ is known. Then, the log-likelihood for the mode...

This paper considers double generalized linear models, which allow the mean and dispersion to be modelled simultaneously in a generalized linear model context. Estimation of the dispersion parameters is based on a χ1 approximation to the unit deviances, and the accuracy of the saddle-point approximation which underlies this is discussed. Approximate REML methods are developed for estimation of ...

• The Birnbaum–Saunders (BS) model is a fatigue life distribution related to the normal one with appealing properties. It is a non-negative transformation of a N(0,1) random variable Z, and its extended version, the so-called generalized Birnbaum– Saunders (GBS) model, obtained replacing Z by any other symmetric continuous random variable, shares the same properties. In this paper we characteri...

We study the main operations (argument shift, differentiation, etc.) in generalized spaces of type S and some classes analytic functions pseudodifferential operators this kind, as well properties Fourier transforms functions, convolutions, convolvers, multiplicators. The correct solvability nonlocal time problem is proved for one class equations S. Its solution presented form convolution fundam...