In this paper we extend the Weibull power series (WPS) class of distributions and named this new class as extended Weibull power series (EWPS) class of distributions. The EWPS distributions are related to series and parallel systems with a random num
- ber of components, whereas the WPS distributions (Morais and Barreto-Souza, 2011) are related to series systems only. Unlike the WPS distributions, for which the Weibull is a limiting special case, the Weibull law is a particular case of the EWPS distributions. We prove that the distributions in this class are identifiable under a simple assumption. We also prove stochastic and hazard rate order results and highlight that the shapes of the EWPS distributions are markedly more flexible than the shapes of the WPS distributions. We define a regression model for the EWPS response random variable to model a scale parameter and its quantiles. We present the maximum likelihood estimator and prove its consistency and normal asymptotic distribution. Although the construction of this class was motivated by series and parallel systems, the EWPS distributions are suitable for modeling a wide range of positive data sets. To illustrate potential uses of this model, we apply it to a real data set on the tensile strength of coconut fibers and present a simple device for diagnostic purposes.
We derive adjusted signed likelihood ratio statistics for a general class of extreme value regression models. The adjustments reduce the error in the standard normal approximation to the distribution of the signed likelihood ratio statistic. We use M
onte Carlo simulations to compare the finite-sample performance of the different tests. Our simulations suggest that the signed likelihood ratio test tends to be liberal when the sample size is not large, and that the adjustments are effective in shrinking the size distortion. Two real data applications are presented and discussed.
Beta regression models provide an adequate approach for modeling continuous outcomes limited to the interval (0,1). This paper deals with an extension of beta regression models that allow for explanatory variables to be measured with error. The struc
tural approach, in which the covariates measured with error are assumed to be random variables, is employed. Three estimation methods are presented, namely maximum likelihood, maximum pseudo-likelihood and regression calibration. Monte Carlo simulations are used to evaluate the performance of the proposed estimators and the naive estimator. Also, a residual analysis for beta regression models with measurement errors is proposed. The results are illustrated in a real data set.
We obtain an asymptotic expansion for the null distribution function of thegradient statistic for testing composite null hypotheses in the presence of nuisance parameters. The expansion is derived using a Bayesian route based on the shrinkage argumen
t described in Ghosh and Mukerjee (1991). Using this expansion, we propose a Bartlett-type corrected gradient statistic with chi-square distribution up to an error of order o(n^{-1}) under the null hypothesis. Further, we also use the expansion to modify the percentage points of the large sample reference chi-square distribution. A small Monte Carlo experiment and various examples are presented and discussed.
In this paper, we develop modifi
We deal with a general class of extreme-value regression models introduced by Barreto- Souza and Vasconcellos (2011). Our goal is to derive an adjusted likelihood ratio statistic that is approximately distributed as c{hi}2 with a high degree of accur
acy. Although the adjusted statistic requires more computational effort than its unadjusted counterpart, it is shown that the adjustment term has a simple compact form that can be easily implemented in standard statistical software. Further, we compare the finite sample performance of the three classical tests (likelihood ratio, Wald, and score), the gradient test that has been recently proposed by Terrell (2002), and the adjusted likelihood ratio test obtained in this paper. Our simulations favor the latter. Applications of our results are presented. Key words: Extreme-value regression; Gradient test; Gumbel distribution; Likelihood ratio test; Nonlinear models; Score test; Small-sample adjustments; Wald test.
In this paper we obtain an adjusted version of the likelihood ratio test for errors-in-variables multivariate linear regression models. The error terms are allowed to follow a multivariate distribution in the class of the elliptical distributions, wh
ich has the multivariate normal distribution as a special case. We derive a modified likelihood ratio statistic that follows a chi-squared distribution with a high degree of accuracy. Our results generalize those in Melo and Ferrari(Advances in Statistical Analysis, 2010, 94, 75-87) by allowing the parameter of interest to be vector-valued in the multivariate errors-in-variables model. We report a simulation study which shows that the proposed test displays superior finite sample behavior relative to the standard likelihood ratio test.
The Birnbaum-Saunders regression model is commonly used in reliability studies. We address the issue of performing inference in this class of models when the number of observations is small. We show that the likelihood ratio test tends to be liberal
when the sample size is small, and we obtain a correction factor which reduces the size distortion of the test. The correction makes the error rate of he test vanish faster as the sample size increases. The numerical results show that the modified test is more reliable in finite samples than the usual likelihood ratio test. We also present an empirical application.
