Robust modeling using the generalized epsilon-skew-t distribution

In this paper, an alternative skew Student-t family of distributions is studied. It is obtained as an extension of the generalized Student-t (GS-t) family introduced by McDonald and Newey [10]. The extension that is obtained can be seen as a reparametrization of the skewed GS-t distribution considered by Theodossiou [14]. A key element in the construction of such an extension is that it can be stochastically represented as a mixture of an epsilon-skew-power-exponential distribution [1] and a generalized-gamma distribution. From this representation, we can readily derive theoretical properties and easy-to-implement simulation schemes. Furthermore, we study some of its main properties including stochastic representation, moments and asymmetry and kurtosis coefficients. We also derive the Fisher information matrix, which is shown to be nonsingular for some special cases such as when the asymmetry parameter is null, that is, at the vicinity of symmetry, and discuss maximum-likelihood estimation. Simulation studies for some particular cases and real data analysis are also reported, illustrating the usefulness of the extension considered.

The new class of Kummer beta generalized distributions

Ng and Kotz (1995) introduced a distribution that provides greater flexibility to extremes. We define and study a new class of distributions called the Kummer beta generalized family to extend the normal, Weibull, gamma and Gumbel distributions, among several other well-known distributions. Some special models are discussed. The ordinary moments of any distribution in the new family can be expressed as linear functions of probability weighted moments of the baseline distribution. We examine the asymptotic distributions of the extreme values. We derive the density function of the order statistics, mean absolute deviations and entropies. We use maximum likelihood estimation to fit the distributions in the new class and illustrate its potentiality with an application to a real data set.

Bartlett corrections in Birnbaum-Saunders nonlinear regression models

Lemonte and Cordeiro [Birnbaum-Saunders nonlinear regression models, Comput. Stat. Data Anal. 53 (2009), pp. 4441-4452] introduced a class of Birnbaum-Saunders (BS) nonlinear regression models potentially useful in lifetime data analysis. We give a general matrix Bartlett correction formula to improve the likelihood ratio (LR) tests in these models. The formula is simple enough to be used analytically to obtain several closed-form expressions in special cases. Our results generalize those in Lemonte et al. [Improved likelihood inference in Birnbaum-Saunders regressions, Comput. Stat. DataAnal. 54 (2010), pp. 1307-1316], which hold only for the BS linear regression models. We consider Monte Carlo simulations to show that the corrected tests work better than the usual LR tests.

The polysurvival model with long-term survivors

Long-term survival models have historically been considered for analyzing time-to-event data with long-term survivors fraction. However, situations in which a fraction (1 - p) of systems is subject to failure from independent competing causes of failure, while the remaining proportion p is cured or has not presented the event of interest during the time period of the study, have not been fully considered in the literature. In order to accommodate such situations, we present in this paper a new long-term survival model. Maximum likelihood estimation procedure is discussed as well as interval estimation and hypothesis tests. A real dataset illustrates the methodology.

The McDonald extended distribution: properties and applications

We study a five-parameter lifetime distribution called the McDonald extended exponential model to generalize the exponential, generalized exponential, Kumaraswamy exponential and beta exponential distributions, among others. We obtain explicit expressions for the moments and incomplete moments, quantile and generating functions, mean deviations, Bonferroni and Lorenz curves and Gini concentration index. The method of maximum likelihood and a Bayesian procedure are adopted for estimating the model parameters. The applicability of the new model is illustrated by means of a real data set.

A log-linear regression model for the beta-Birnbaum-Saunders distribution with censored data

The beta-Birnbaum-Saunders (Cordeiro and Lemonte, 2011) and Birnbaum-Saunders (Birnbaum and Saunders, 1969a) distributions have been used quite effectively to model failure times for materials subject to fatigue and lifetime data. We define the log-beta-Birnbaum-Saunders distribution by the logarithm of the beta-Birnbaum-Saunders distribution. Explicit expressions for its generating function and moments are derived. We propose a new log-beta-Birnbaum-Saunders regression model that can be applied to censored data and be used more effectively in survival analysis. We obtain the maximum likelihood estimates of the model parameters for censored data and investigate influence diagnostics. The new location-scale regression model is modified for the possibility that long-term survivors may be presented in the data. Its usefulness is illustrated by means of two real data sets. (C) 2011 Elsevier B.V. All rights reserved.

Influence diagnostics in Gaussian spatial linear models

Spatial linear models have been applied in numerous fields such as agriculture, geoscience and environmental sciences, among many others. Spatial dependence structure modelling, using a geostatistical approach, is an indispensable tool to estimate the parameters that define this structure. However, this estimation may be greatly affected by the presence of atypical observations in the sampled data. The purpose of this paper is to use diagnostic techniques to assess the sensitivity of the maximum-likelihood estimators, covariance functions and linear predictor to small perturbations in the data and/or the spatial linear model assumptions. The methodology is illustrated with two real data sets. The results allowed us to conclude that the presence of atypical values in the sample data have a strong influence on thematic maps, changing the spatial dependence structure.

Robust statistical modeling using the Birnbaum-Saunders-t distribution applied to insurance

In this paper, we carry out robust modeling and influence diagnostics in Birnbaum-Saunders (BS) regression models. Specifically, we present some aspects related to BS and log-BS distributions and their generalizations from the Student-t distribution, and develop BS-t regression models, including maximum likelihood estimation based on the EM algorithm and diagnostic tools. In addition, we apply the obtained results to real data from insurance, which shows the uses of the proposed model. Copyright (c) 2011 John Wiley & Sons, Ltd.

A general class of zero-or-one inflated beta regression models

This paper proposes a general class of regression models for continuous proportions when the data contain zeros or ones. The proposed class of models assumes that the response variable has a mixed continuous-discrete distribution with probability mass at zero or one. The beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. We use a suitable parameterization of the beta law in terms of its mean and a precision parameter. The parameters of the mixture distribution are modeled as functions of regression parameters. We provide inference, diagnostic, and model selection tools for this class of models. A practical application that employs real data is presented. (C) 2011 Elsevier B.V. All rights reserved.

Semiparametric Normal Transformation Models for Spatially Correlated Survival Data

There is an emerging interest in modeling spatially correlated survival data in biomedical and epidemiological studies. In this paper, we propose a new class of semiparametric normal transformation models for right censored spatially correlated survival data. This class of models assumes that survival outcomes marginally follow a Cox proportional hazard model with unspecified baseline hazard, and their joint distribution is obtained by transforming survival outcomes to normal random variables, whose joint distribution is assumed to be multivariate normal with a spatial correlation structure. A key feature of the class of semiparametric normal transformation models is that it provides a rich class of spatial survival models where regression coefficients have population average interpretation and the spatial dependence of survival times is conveniently modeled using the transformed variables by flexible normal random fields. We study the relationship of the spatial correlation structure of the transformed normal variables and the dependence measures of the original survival times. Direct nonparametric maximum likelihood estimation in such models is practically prohibited due to the high dimensional intractable integration of the likelihood function and the infinite dimensional nuisance baseline hazard parameter. We hence develop a class of spatial semiparametric estimating equations, which conveniently estimate the population-level regression coefficients and the dependence parameters simultaneously. We study the asymptotic properties of the proposed estimators, and show that they are consistent and asymptotically normal. The proposed method is illustrated with an analysis of data from the East Boston Ashma Study and its performance is evaluated using simulations.

Laser Thomson scattering measurements of electron temperature and density in a Hall-effect plasma

Hall-effect thrusters (HETs) are compact electric propulsion devices with high specific impulse used for a variety of space propulsion applications. HET technology is well developed but the electron properties in the discharge are not completely understood, mainly due to the difficulty involved in performing accurate measurements in the discharge. Measurements of electron temperature and density have been performed using electrostatic probes, but presence of the probes can significantly disrupt thruster operation, and thus alter the electron temperature and density. While fast-probe studies have expanded understanding of HET discharges, a non-invasive method of measuring the electron temperature and density in the plasma is highly desirable. An alternative to electrostatic probes is a non-perturbing laser diagnostic technique that measures Thomson scattering from the plasma. Thomson scattering is the process by which photons are elastically scattered from the free electrons in a plasma. Since the electrons have thermal energy their motion causes a Doppler shift in the scattered photons that is proportional to their velocity. Like electrostatic probes, laser Thomson scattering (LTS) can be used to determine the temperature and density of free electrons in the plasma. Since Thomson scattering measures the electron velocity distribution function directly no assumptions of the plasma conditions are required, allowing accurate measurements in anisotropic and non-Maxwellian plasmas. LTS requires a complicated measurement apparatus, but has the potential to provide accurate, non-perturbing measurements of electron temperature and density in HET discharges. In order to assess the feasibility of LTS diagnostics on HETs non-invasive measurements of electron temperature and density in the near-field plume of a Hall thruster were performed using a custom built laser Thomson scattering diagnostic. Laser measurements were processed using a maximum likelihood estimation method and results were compared to conventional electrostatic double probe measurements performed at the same thruster conditions. Electron temperature was found to range from approximately 1 – 40 eV and density ranged from approximately 1.0 x 1017 m-3 to 1.3 x 1018 m-3 over discharge voltages from 250 to 450 V and mass flow rates of 40 to 80 SCCM using xenon propellant.

Integration of Truncated Distributions in Exponential Family with Simulation Models of Logistics and Supply Chain Management

Truncated distributions of the exponential family have great influence in the simulation models. This paper discusses the truncated Weibull distribution specifically. The truncation of the distribution is achieved by the Maximum Likelihood Estimation method or combined with the expectation and variance expressions. After the fitting of distribution, the goodness-of-fit tests (the Chi-Square test and the Kolmogorov-Smirnov test) are executed to rule out the rejected hypotheses. Finally the distributions are integrated in various simulation models, e. g. shipment consolidation model, to compare the influence of truncated and original versions of Weibull distribution on the model.

Population genetics of VNTR loci and their applications in evolutionary studies

Variable number of tandem repeats (VNTR) are genetic loci at which short sequence motifs are found repeated different numbers of times among chromosomes. To explore the potential utility of VNTR loci in evolutionary studies, I have conducted a series of studies to address the following questions: (1) What are the population genetic properties of these loci? (2) What are the mutational mechanisms of repeat number change at these loci? (3) Can DNA profiles be used to measure the relatedness between a pair of individuals? (4) Can DNA fingerprint be used to measure the relatedness between populations in evolutionary studies? (5) Can microsatellite and short tandem repeat (STR) loci which mutate stepwisely be used in evolutionary analyses?^ A large number of VNTR loci typed in many populations were studied by means of statistical methods developed recently. The results of this work indicate that there is no significant departure from Hardy-Weinberg expectation (HWE) at VNTR loci in most of the human populations examined, and the departure from HWE in some VNTR loci are not solely caused by the presence of population sub-structure.^ A statistical procedure is developed to investigate the mutational mechanisms of VNTR loci by studying the allele frequency distributions of these loci. Comparisons of frequency distribution data on several hundreds VNTR loci with the predictions of two mutation models demonstrated that there are differences among VNTR loci grouped by repeat unit sizes.^ By extending the ITO method, I derived the distribution of the number of shared bands between individuals with any kinship relationship. A maximum likelihood estimation procedure is proposed to estimate the relatedness between individuals from the observed number of shared bands between them.^ It was believed that classical measures of genetic distance are not applicable to analysis of DNA fingerprints which reveal many minisatellite loci simultaneously in the genome, because the information regarding underlying alleles and loci is not available. I proposed a new measure of genetic distance based on band sharing between individuals that is applicable to DNA fingerprint data.^ To address the concern that microsatellite and STR loci may not be useful for evolutionary studies because of the convergent nature of their mutation mechanisms, by a theoretical study as well as by computer simulation, I conclude that the possible bias caused by the convergent mutations can be corrected, and a novel measure of genetic distance that makes the correction is suggested. In summary, I conclude that hypervariable VNTR loci are useful in evolutionary studies of closely related populations or species, especially in the study of human evolution and the history of geographic dispersal of Homo sapiens. (Abstract shortened by UMI.) ^

Analysis of recurrent failure times: A time-dependent Yule process approach

Analysis of recurrent events has been widely discussed in medical, health services, insurance, and engineering areas in recent years. This research proposes to use a nonhomogeneous Yule process with the proportional intensity assumption to model the hazard function on recurrent events data and the associated risk factors. This method assumes that repeated events occur for each individual, with given covariates, according to a nonhomogeneous Yule process with intensity function λx(t) = λ 0(t) · exp( x′β). One of the advantages of using a non-homogeneous Yule process for recurrent events is that it assumes that the recurrent rate is proportional to the number of events that occur up to time t. Maximum likelihood estimation is used to provide estimates of the parameters in the model, and a generalized scoring iterative procedure is applied in numerical computation. ^ Model comparisons between the proposed method and other existing recurrent models are addressed by simulation. One example concerning recurrent myocardial infarction events compared between two distinct populations, Mexican-American and Non-Hispanic Whites in the Corpus Christi Heart Project is examined. ^

Outcome-based adaptive randomization for binary data in clinical trials---Compare and contrast

Monte Carlo simulation has been conducted to investigate parameter estimation and hypothesis testing in some well known adaptive randomization procedures. The four urn models studied are Randomized Play-the-Winner (RPW), Randomized Pôlya Urn (RPU), Birth and Death Urn with Immigration (BDUI), and Drop-the-Loses Urn (DL). Two sequential estimation methods, the sequential maximum likelihood estimation (SMLE) and the doubly adaptive biased coin design (DABC), are simulated at three optimal allocation targets that minimize the expected number of failures under the assumption of constant variance of simple difference (RSIHR), relative risk (ORR), and odds ratio (OOR) respectively. Log likelihood ratio test and three Wald-type tests (simple difference, log of relative risk, log of odds ratio) are compared in different adaptive procedures. ^ Simulation results indicates that although RPW is slightly better in assigning more patients to the superior treatment, the DL method is considerably less variable and the test statistics have better normality. When compared with SMLE, DABC has slightly higher overall response rate with lower variance, but has larger bias and variance in parameter estimation. Additionally, the test statistics in SMLE have better normality and lower type I error rate, and the power of hypothesis testing is more comparable with the equal randomization. Usually, RSIHR has the highest power among the 3 optimal allocation ratios. However, the ORR allocation has better power and lower type I error rate when the log of relative risk is the test statistics. The number of expected failures in ORR is smaller than RSIHR. It is also shown that the simple difference of response rates has the worst normality among all 4 test statistics. The power of hypothesis test is always inflated when simple difference is used. On the other hand, the normality of the log likelihood ratio test statistics is robust against the change of adaptive randomization procedures. ^