68 research outputs found
A log-Birnbaum-Saunders Regression Model with Asymmetric Errors
The paper by Leiva et al. (2010) introduced a skewed version of the
sinh-normal distribution, discussed some of its properties and characterized an
extension of the Birnbaum-Saunders distribution associated with this
distribution. In this paper, we introduce a skewed log-Birnbaum-Saunders
regression model based on the skewed sinh-normal distribution. Some influence
methods, such as the local influence and generalized leverage are presented.
Additionally, we derived the normal curvatures of local influence under some
perturbation schemes. An empirical application to a real data set is presented
in order to illustrate the usefulness of the proposed model.Comment: Submitted for publicatio
Local power of the LR, Wald, score and gradient tests in dispersion models
We derive asymptotic expansions up to order for the nonnull
distribution functions of the likelihood ratio, Wald, score and gradient test
statistics in the class of dispersion models, under a sequence of Pitman
alternatives. The asymptotic distributions of these statistics are obtained for
testing a subset of regression parameters and for testing the precision
parameter. Based on these nonnull asymptotic expansions it is shown that there
is no uniform superiority of one test with respect to the others for testing a
subset of regression parameters. Furthermore, in order to compare the
finite-sample performance of these tests in this class of models, Monte Carlo
simulations are presented. An empirical application to a real data set is
considered for illustrative purposes.Comment: Submitted for publicatio
Size and power properties of some tests in the Birnbaum-Saunders regression model
The Birnbaum-Saunders distribution has been used quite effectively to model
times to failure for materials subject to fatigue and for modeling lifetime
data. In this paper we obtain asymptotic expansions, up to order and
under a sequence of Pitman alternatives, for the nonnull distribution functions
of the likelihood ratio, Wald, score and gradient test statistics in the
Birnbaum-Saunders regression model. The asymptotic distributions of all four
statistics are obtained for testing a subset of regression parameters and for
testing the shape parameter. Monte Carlo simulation is presented in order to
compare the finite-sample performance of these tests. We also present an
empirical application.Comment: Paper submitted for publication, with 13 pages and 1 figur
On Goodness-of-Fit Tests for the Neyman Type A Distribution
The two-parameter Neyman type A distribution is quite useful for modeling count data, since it corresponds to a simple, flexible and overdispersed discrete distribution, which is also zero[1]inflated. In this paper, we show that the probability generating function of the Neyman type A distribution is the only probability generating function which satisfies a certain differential equation. Based on an empirical counterpart of this specific differential equation, we propose and study a new goodness-of-fit test for this distribution. The test is consistent against fixed alternative hypotheses, while its null distribution can be consistently approximated by using parametric bootstrap. We investigate the finite sample performance of the proposed test numerically by means of Monte Carlo experiments, and comparisons with other existing goodness-of-fit tests are also considered. Empirical applications to real data are considered for illustrative purposes
The Beta-Half-Cauchy Distribution
On the basis of the half-Cauchy distribution, we propose the called beta-half-Cauchy distribution for modeling lifetime data. Various explicit expressions for its moments, generating and quantile functions, mean deviations, and density function of the order statistics and their moments are provided. The parameters of the new model are estimated by maximum likelihood, and the observed information matrix is derived. An application to lifetime real data shows that it can yield a better fit than three-and two-parameter Birnbaum-Saunders, gamma, and Weibull models
Testing hypotheses in the Birnbaum-Saunders distribution under type-II censored samples
The two-parameter Birnbaum-Saunders distribution has been used succesfully to
model fatigue failure times. Although censoring is typical in reliability and
survival studies, little work has been published on the analysis of censored
data for this distribution. In this paper, we address the issue of performing
testing inference on the two parameters of the Birnbaum-Saunders distribution
under type-II right censored samples. The likelihood ratio statistic and a
recently proposed statistic, the gradient statistic, provide a convenient
framework for statistical inference in such a case, since they do not require
to obtain, estimate or invert an information matrix, which is an advantage in
problems involving censored data. An extensive Monte Carlo simulation study is
carried out in order to investigate and compare the finite sample performance
of the likelihood ratio and the gradient tests. Our numerical results show
evidence that the gradient test should be preferred. Three empirical
applications are presented.Comment: Submitted for publicatio
Small-sample corrections for score tests in Birnbaum-Saunders regressions
In this paper we deal with the issue of performing accurate small-sample
inference in the Birnbaum-Saunders regression model, which can be useful for
modeling lifetime or reliability data. We derive a Bartlett-type correction for
the score test and numerically compare the corrected test with the usual score
test, the likelihood ratio test and its Bartlett-corrected version. Our
simulation results suggest that the corrected test we propose is more reliable
than the other tests.Comment: To appear in the Communications in Statistics - Theory and Methods,
http://www.informaworld.com/smpp/title~content=t71359723
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