The McDonald inverted beta distribution

We introduce a five-parameter continuous model, called the McDonald inverted beta distribution, to extend the two-parameter inverted beta distribution and provide new four- and three-parameter sub-models. We give a mathematical treatment of the new distribution including expansions for the density function, moments, generating and quantile functions, mean deviations, entropy and reliability. The model parameters are estimated by maximum likelihood and the observed information matrix is derived. An application of the new model to real data shows that it can give consistently a better fit than other important lifetime models. (C) 2012 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

General results for the Kumaraswamy-G distribution

For any continuous baseline G distribution [G. M. Cordeiro and M. de Castro, A new family of generalized distributions, J. Statist. Comput. Simul. 81 (2011), pp. 883-898], proposed a new generalized distribution (denoted here with the prefix 'Kw-G'(Kumaraswamy-G)) with two extra positive parameters. They studied some of its mathematical properties and presented special sub-models. We derive a simple representation for the Kw-Gdensity function as a linear combination of exponentiated-G distributions. Some new distributions are proposed as sub-models of this family, for example, the Kw-Chen [Z.A. Chen, A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statist. Probab. Lett. 49 (2000), pp. 155-161], Kw-XTG [M. Xie, Y. Tang, and T.N. Goh, A modified Weibull extension with bathtub failure rate function, Reliab. Eng. System Safety 76 (2002), pp. 279-285] and Kw-Flexible Weibull [M. Bebbington, C. D. Lai, and R. Zitikis, A flexible Weibull extension, Reliab. Eng. System Safety 92 (2007), pp. 719-726]. New properties of the Kw-G distribution are derived which include asymptotes, shapes, moments, moment generating function, mean deviations, Bonferroni and Lorenz curves, reliability, Renyi entropy and Shannon entropy. New properties of the order statistics are investigated. We discuss the estimation of the parameters by maximum likelihood. We provide two applications to real data sets and discuss a bivariate extension of the Kw-G distribution.

INFERENCES FOR THE CHANGE-POINT OF THE EXPONENTIATED WEIBULL HAZARD FUNCTION

In many applications of lifetime data analysis, it is important to perform inferences about the change-point of the hazard function. The change-point could be a maximum for unimodal hazard functions or a minimum for bathtub forms of hazard functions and is usually of great interest in medical or industrial applications. For lifetime distributions where this change-point of the hazard function can be analytically calculated, its maximum likelihood estimator is easily obtained from the invariance properties of the maximum likelihood estimators. From the asymptotical normality of the maximum likelihood estimators, confidence intervals can also be obtained. Considering the exponentiated Weibull distribution for the lifetime data, we have different forms for the hazard function: constant, increasing, unimodal, decreasing or bathtub forms. This model gives great flexibility of fit, but we do not have analytic expressions for the change-point of the hazard function. In this way, we consider the use of Markov Chain Monte Carlo methods to get posterior summaries for the change-point of the hazard function considering the exponentiated Weibull distribution.

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.

Cardiogoniometric parameters for detection of coronary artery disease at rest as a function of stenosis localization and distribution

Cardiogoniometry (CGM), a spatiotemporal electrocardiologic 5-lead method with automated analysis, may be useful in primary healthcare for detecting coronary artery disease (CAD) at rest. Our aim was to systematically develop a stenosis-specific parameter set for global CAD detection. In 793 consecutively admitted patients with presumed non-acute CAD, CGM data were collected prior to elective coronary angiography and analyzed retrospectively. 658 patients fulfilled the inclusion criteria, 405 had CAD verified by coronary angiography; the 253 patients with normal coronary angiograms served as the non-CAD controls. Study patients--matched for age, BMI, and gender--were angiographically assigned to 8 stenosis-specific CAD categories or to the controls. One CGM parameter possessing significance (P < .05) and the best diagnostic accuracy was matched to one CAD category. The area under the ROC curve was .80 (global CAD versus controls). A set containing 8 stenosis-specific CGM parameters described variability of R vectors and R-T angles, spatial position and potential distribution of R/T vectors, and ST/T segment alterations. Our parameter set systematically combines CAD categories into an algorithm that detects CAD globally. Prospective validation in clinical studies is ongoing.

New Results Concerning Probability Distributions with Increasing Generalized Failure Rates

The generalized failure rate of a continuous random variable has demonstrable importance in operations management. If the valuation distribution of a product has an increasing generalized failure rate (that is, the distribution is IGFR), then the associated revenue function is unimodal, and when the generalized failure rate is strictly increasing, the global maximum is uniquely specified. The assumption that the distribution is IGFR is thus useful and frequently held in recent pricing, revenue, and supply chain management literature. This note contributes to the IGFR literature in several ways. First, it investigates the prevalence of the IGFR property for the left and right truncations of valuation distributions. Second, we extend the IGFR notion to discrete distributions and contrast it with the continuous distribution case. The note also addresses two errors in the previous IGFR literature. Finally, for future reference, we analyze all common (continuous and discrete) distributions for the prevalence of the IGFR property, and derive and tabulate their generalized failure rates.

Concordance Probability and Discriminatory Power in Proportional Hazards Regression

The concordance probability is used to evaluate the discriminatory power and the predictive accuracy of nonlinear statistical models. We derive an analytic expression for the concordance probability in the Cox proportional hazards model. The proposed estimator is a function of the regression parameters and the covariate distribution only and does not use the observed event and censoring times. For this reason it is asymptotically unbiased, unlike Harrell's c-index based on informative pairs. The asymptotic distribution of the concordance probability estimate is derived using U-statistic theory and the methodology is applied to a predictive model in lung cancer.

Reliability studies of the skew normal distribution

It has been observed in various practical applications that data do not conform to the normal distribution, which is symmetric with no skewness. The skew normal distribution proposed by Azzalini(1985) is appropriate for the analysis of data which is unimodal but exhibits some skewness. The skew normal distribution includes the normal distribution as a special case where the skewness parameter is zero. In this thesis, we study the structural properties of the skew normal distribution, with an emphasis on the reliability properties of the model. More specifically, we obtain the failure rate, the mean residual life function, and the reliability function of a skew normal random variable. We also compare it with the normal distribution with respect to certain stochastic orderings. Appropriate machinery is developed to obtain the reliability of a component when the strength and stress follow the skew normal distribution. Finally, IQ score data from Roberts (1988) is analyzed to illustrate the procedure.

Brush border myosin-I truncated in the motor domain impairs the distribution and the function of endocytic compartments in an hepatoma cell line.

Myosins I, a ubiquitous monomeric class of myosins that exhibits actin-based motor properties, are associated with plasma and/or vesicular membranes and have been suggested as players for trafficking events between cell surface and intracellular membranous structures. To investigate the function of myosins 1, we have transfected a mouse hepatoma cell line (BWTG3) with cDNAs encoding the chicken brush border myosin-I (BBMI) and two variants truncated in the motor domain. One variant is deleted of the first 446 amino acids and thereby lacks the ATP binding site, whereas the other is deleted of the entire motor domain and lacks the ATP and actin binding sites. We have observed (i) that significant amounts of the truncated variants are recovered with membrane fractions after cell fractionation, (ii) that they codistribute with a compartment containing alpha2-macroglobulin internalized for 30 min as determined by fluorescent microscopy, (iii) that the production of BBMI-truncated variants impairs the distribution of the acidic compartment and ligands internalized for 30 min, and (iv) that the production of the truncated variant containing the actin binding site decreases the rate of alpha2-macroglobulin degradation whereas the production of the variant lacking the ATP binding site and the actin binding site increases the rate of a2-macroglobulin degradation. These observations indicate that the two truncated variants have a dominant negative effect on the distribution and the function of the endocytic compartments. We propose that an unidentified myosin-I might contribute to the distribution of endocytic compartments in a juxtanuclear position and/or to the regulation of the delivery of ligands to the degradative compartment in BWTG3 cells.

Ring Out Your Dead : Distribution, form, and function of iron amulets in the late Iron Age grave fields of Lovö

The purpose of this study is to analyze the distribution, forms, and function(s) of iron amulets deposited in the late Iron Age gravefields of Lovö, with the goal of ascertaining how (and so far as possible why) these objects were utilized in rituals carried out during and after burials. Particular emphasis is given to re-interpreting the largest group of iron amulets, the iron amulet rings, in a more relational and practice-focused way than has heretofore been attempted. By framing burial analyses, questions of typology, and evidence of ritualized actions in comparison with what is known of other cult sites in Mälardalen specifically– and theorized about the cognitive landscape(s) of late Iron Age Scandinavia generally– a picture of iron amulets as inscribed objects made to act as catalytic, protective, and mediating agents is brought to light.