In this paper, we derive a simple matrix formula for second-order covariances of maximum likelihood estimates in generalized linear models. The formula covers many important and commonly used models and is also simple enough to be used algebraically to obtain closed-form expressions in special...

We give general formulae using matrix notation for computing Bartlett corrections for the likelihood ratio statistics in two quite distinct situations. In the first, we consider the test of a null hypothesis, which specifies a parameter vector, in the presence of nuisance parameters. In the...

A rigorous asymptotic theory for Pearson residuals in generalized linear models is not yet available. We give matrix formulae of order n-1, where n is the sample size, for the first two moments of these residuals. The formulae are applicable to many regression models in common use. We suggest...

Under suitable regularity conditions, an improved score test was derived by Cordeiro and Ferrari (1991). The test is based on a corrected score statistic which has a chi-squared distribution to order n-1 under the null hypothesis, where n is the sample size. In this paper we follow their...

In this paper we derive second- and third-order bias-corrected maximum likelihood estimates in general uniparametric models. We compare the corrected estimates and the usual maximum likelihood estimate in terms of their mean squared errors. We also obtain closed-form expressions for...

In this paper, we formulate a flexible density function from the selection mechanism viewpoint (see, for example, Bayarri and DeGroot (1992) and Arellano-Valle et al. (2006)) which possesses nice biological and physical interpretations. The new density function contains as special cases many...

In this article, for the first time, we propose the negative binomial--beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model...

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...

Birnbaum and Saunders (1969a) introduced a probability distribution which is commonly used in reliability studies. For the first time, based on this distribution, the so-called [beta]-Birnbaum-Saunders distribution is proposed for fatigue life modeling. Various properties of the new model...