For the first time, we give an asymptotic formula of order n-2, where n is the sample size, for the covariance matrix of the maximum likelihood estimators of the regression parameters in regular dispersion models. The covariance matrix formula does not involve cumulants of log-likelihood...

The family of distributions proposed by Birnbaum and Saunders (1969) can be used to model lifetime data and it is widely applicable to model failure times of fatiguing materials. We give a simple matrix formula of order n-1/2, where n is the sample size, for the skewness of the distributions...

We introduce in this paper a new class of discrete generalized nonlinear models to extend the binomial, Poisson and negative binomial models to cope with count data. This class of models includes some important models such as log-nonlinear models, logit, probit and negative binomial nonlinear...

A bathtub-shaped failure rate function is very useful in survival analysis and reliability studies. The well-known lifetime distributions do not have this property. For the first time, we propose a location-scale regression model based on the logarithm of an extended Weibull distribution which...

In general, the distribution of residuals cannot be obtained explicitly. In this paper we give an asymptotic formula for the density of Pearson residuals in continuous generalized linear models corrected to order n-1, where n is the sample size. We define a set of corrected Pearson residuals for...

We introduce, for the first time, a new class of Birnbaum-Saunders nonlinear regression models potentially useful in lifetime data analysis. The class generalizes the regression model described by Rieck and Nedelman [Rieck, J.R., Nedelman, J.R., 1991. A log-linear model for the Birnbaum-Saunders...

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in...

In this paper, we derive general formulae for second-order biases of maximum likelihood estimates which can be applied to a wide class of multivariate nonlinear regression models. The class of models we consider is very rich and includes a number of commonly used models in econometrics and...

For the first time, a five-parameter distribution, the so-called beta Burr XII distribution, is defined and investigated. The new distribution contains as special sub-models some well-known distributions discussed in the literature, such as the logistic, Weibull and Burr XII distributions, among...