219 research outputs found
An R Package for a General Class of Inverse Gaussian Distributions
The inverse Gaussian distribution is a positively skewed probability model that has received great attention in the last 20 years. Recently, a family that generalizes this model called inverse Gaussian type distributions has been developed. The new R package named ig has been designed to analyze data from inverse Gaussian type distributions. This package contains basic probabilistic functions, lifetime indicators and a random number generator from this model. Also, parameter estimates and diagnostics analysis can be obtained using likelihood methods by means of this package. In addition, goodness-of-fit methods are implemented in order to detect the suitability of the model to the data. The capabilities and features of the ig package are illustrated using simulated and real data sets. Furthermore, some new results related to the inverse Gaussian type distribution are also obtained. Moreover, a simulation study is conducted for evaluating the estimation method implemented in the ig package.
An overview of kriging and cokriging predictors for functional random fields
This article presents an overview of methodologies for spatial prediction of functional data,
focusing on both stationary and non-stationary conditions. A significant aspect of the functional
random fields analysis is evaluating stationarity to characterize the stability of statistical properties
across the spatial domain. The article explores methodologies from the literature, providing insights
into the challenges and advancements in functional geostatistics. This work is relevant from theoreti cal and practical perspectives, offering an integrated view of methodologies tailored to the specific
stationarity conditions of the functional processes under study. The practical implications of our
work span across fields like environmental monitoring, geosciences, and biomedical research. This
overview encourages advancements in functional geostatistics, paving the way for the development
of innovative techniques for analyzing and predicting spatially correlated functional data. It lays the
groundwork for future research, enhancing our understanding of spatial statistics and its applications.This research was partially supported by FONDECYT, grant number 1200525 (V.L.), from the National Agency for Research and Development (ANID) of the Chilean government under the Ministry of Science, Technology, Knowledge, and Innovation; and by Portuguese funds through the CMAT—Research Centre of Mathematics of University of Minho—within projects UIDB/00013/2020 and UIDP/00013/2020 (C.C.)
On an extreme value version of the Birnbaum-Saunders distribution
The Birnbaum-Saunders model is a life distribution originated from a problem of
material fatigue that has been largely studied and applied in recent decades. A
random variable following the Birnbaum-Saunders distribution can be stochastically
represented by another random variable used as basis. Then, the Birnbaum-Saunders
model can be generalized by switching the distribution of the basis variable using
diverse arguments allowing to construct more general classes of models. Extreme value
distributions are useful to determinate the probability of events that are more extreme
than any that have already been observed. In this paper, we propose, characterize,
implement and apply an extreme value version of the Birnbaum-Saunders distribution.Fundação para a Ciência e a Tecnologia (FCT) - Pluriannual Funding Program, PTDC/FEDER, PEst-OE/MAT/UI0006/2011, FCT/OE, POCI 2010FONDECYT (Fondo Nacional
de Desarrollo Cient co y Tecnol ogico - Chile
Estimation in the Birnbaum-Saunders distribution based on scale-mixture of normals and the EM-algorithm
Scale mixtures of normal (SMN) distributions are used for modeling symmetric data. Members
of this family have appealing properties such as robust estimates, easy number generation, and efficient computation of the ML estimates via the EM-algorithm. The Birnbaum-Saunders (BS) distribution is a positively skewed model that is related to the normal distribution and has received
considerable attention. We introduce a type of BS distributions based on SMN models, produce a lifetime analysis, develop the EM-algorithm for ML estimation of parameters, and illustrate the obtained results with real data showing the robustness of the estimation procedure.Peer Reviewe
The extreme value Birnbaum-Saunders model, its moments and an application in biometry
The Birnbaum-Saunders (BS) model is a life distribution that has been
largely studied and applied. Recently, a new version of the BS distribution
based on extreme value theory has been introduced, which is named
extreme value Birnbaum-Saunders (EVBS) distribution. In this article,
we provide some further details on the EVBS models that can be useful
as a supplement to the already existing results. We use these models to
analyze real survival time data of patients treated with alkylating agents
for multiple myeloma. This analysis allow us to show the adequacy of
these new statistical distributions and identify them as models useful for
medical practitioners in order to obtain a prediction of the survival times
of these patients and evaluate changes in the dose of their treatment.Fundação para a Ciência e a Tecnologia (FCT) - Pluriannual Funding Program, PTDC/FEDER, PEst-OE/MAT/UI0006/2011, FCT/OE, POCI 201
The extreme value Birnbaum-Saunders model in athletics
The Birnbaum-Saunders (BS) model is a life distribution that has recently been largely studied and applied. A random variable following the BS distribution can be defined through a simple transformation of a standard normal. The BS model can thus be generalized by switching the standard normal distribution of the basis random variable, allowing the construction of more general classes of models. Among those models, we mention the extreme value Birnbaum-Saunders (EVBS) models, recently introduced in the literature, and
based on results from extreme value theory. A real application to athletics data will be used to illustrate the methodology and to provide the way this model and related models can link with traditional extreme value analysis methods.Este trabalho é financiado por Fundos FEDER através do Programa Operacional Factores de Competitividade - COMPETE e por Fundos Nacionais através da FCT - Fundação para a Ciência e a Tecnologia no
âmbito do projecto PEst-C/MAT/UI0013/2011.Este trabalho é financiado por Fundos FEDER através do Programa Operacional Factores de Competitividade - COMPETE e por Fundos Nacionais através da FCT - Fundação para a Ciência e a Tecnologia no âmbito do projecto PEst-C/MAT/UI0013/2011
Estimation in the Birnbaum-Saunders distribution based on scale-mixture of normals and the EM-algorithm
Scale mixtures of normal (SMN) distributions are used for modeling symmetric data. Members of this family have appealing properties such as robust estimates, easy number generation, and efficient computation of the ML estimates via the EM-algorithm. The Birnbaum-Saunders (BS) distribution is a positively skewed model that is related to the normal distribution and has received considerable attention. We introduce a type of BS distributions based on SMN models, produce a lifetime analysis, develop the EM-algorithm for ML estimation of parameters, and illustrate the obtained results with real data showing the robustness of the estimation procedure
Shape and change point analyses of the Birnbaum-Saunders-t hazard rate and associated estimation
The hazard rate is a statistical indicator commonly used in lifetime analysis. The Birnbaum-Saunders (BS) model is a life distribution originated from a problem pertaining to material fatigue that has been applied to diverse fields. The BS model relates the total time until failure to some type of cumulative damage that is normally distributed. The generalized BS (GBS) distribution is a class of positively skewed models with lighter and heavier tails than the BS distribution. Particular cases of GBS distributions are the BS and BS-Student-t (BS-t) models. In this paper, we discuss shape and change point analyses for the hazard rate of the BS-t distribution. In addition, we evaluate the performance of the maximum likelihood and moment estimators of this change point using Monte Carlo methods. We also present an application with a real life data set useful for survival analysis, which shows the convenience of knowing such instant of change for establishing a reduction in the dose and, as a consequence, in the cost of the treatment.FEDER Funds- Programa
Operacional Factores de Competitividade - COMPETEFundação para a Ciênciae a Tecnologia (FCT) - Project Est-C/MAT/UI0013/2011FONDECYT 1120879 grant, Chil
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