3,846 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
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
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
Snow Cover in Alaska: Comprehensive Review
This report presents the results of a statistical analysis of snow cover in Alaska using historical
data acquired from the Global Historical Climate Network. Measurements of snow depth and
snow water equivalence were collected for Alaska stations between 1950 and 2017. Data
cleaning and a distribution analysis were completed for all stations. Finally regression
equations were developed to estimate snow water equivalence using recorded snow depth
data from Alaska stations.
The project is partially supported by ConocoPhillips Arctic Science and Engineering Foundation,
UAA, and the Structural Engineers Association of Alaska (SEAAK).University of Alaska Anchorage
ConocoPhillips Arctic Science and Engineering Foundation
Structural Engineers Association of AlaskaAbstract / Introduction / Methodology / Discussion / Conclusion / References / Appendix 1 Predicted 50-year WESD Stations's snow laods / Appendix 2 Calcuated 50-Year SNWD Station's snow loads / Appendix 3 Distribution Assignment for WESD and SNWD Stations / Appendix 4 Station Plot
Multivariate Birnbaum-Saunders Distributions: Modelling and Applications
Since its origins and numerous applications in material science, the Birnbaum–Saunders family of distributions has now found widespread uses in some areas of the applied sciences such as agriculture, environment and medicine, as well as in quality control, among others. It is able to model varied data behaviour and hence provides a flexible alternative to the most usual distributions. The family includes Birnbaum–Saunders and log-Birnbaum–Saunders distributions in univariate and multivariate versions. There are now well-developed methods for estimation and diagnostics that allow in-depth analyses. This paper gives a detailed review of existing methods and of relevant literature, introducing properties and theoretical results in a systematic way. To emphasise the range of suitable applications, full analyses are included of examples based on regression and diagnostics in material science, spatial data modelling in agricultural engineering and control charts for environmental monitoring. However, potential future uses in new areas such as business, economics, finance and insurance are also discussed. This work is presented to provide a full tool-kit of novel statistical models and methods to encourage other researchers to implement them in these new areas. It is expected that the methods will have the same positive impact in the new areas as they have had elsewhere
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