The exponentiated generalized gamma distribution with application to lifetime data

A four-parameter extension of the generalized gamma distribution capable of modelling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone and non-monotone failure rate functions, which are quite common in lifetime data analysis and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the exponentiated Weibull, exponentiated generalized half-normal, exponentiated gamma and generalized Rayleigh, among others. We derive two infinite sum representations for its moments. We calculate the density of the order statistics and two expansions for their moments. The method of maximum likelihood is used for estimating the model parameters and the observed information matrix is obtained. Finally, a real data set from the medical area is analysed.

A generalized modified Weibull distribution for lifetime modeling

A four parameter generalization of the Weibull distribution capable of modeling a bathtub-shaped hazard rate function is defined and studied. The beauty and importance of this distribution lies in its ability to model monotone as well as non-monotone failure rates, which are quite common in lifetime problems and reliability. The new distribution has a number of well-known lifetime special sub-models, such as the Weibull, extreme value, exponentiated Weibull, generalized Rayleigh and modified Weibull distributions, among others. We derive two infinite sum representations for its moments. The density of the order statistics is obtained. The method of maximum likelihood is used for estimating the model parameters. Also, the observed information matrix is obtained. Two applications are presented to illustrate the proposed distribution. (C) 2008 Elsevier B.V. All rights reserved.

The complementary exponential power lifetime model

In this paper we propose a new lifetime distribution which can handle bathtub-shaped unimodal increasing and decreasing hazard rate functions The model has three parameters and generalizes the exponential power distribution proposed by Smith and Bain (1975) with the inclusion of an additional shape parameter The maximum likelihood estimation procedure is discussed A small-scale simulation study examines the performance of the likelihood ratio statistics under small and moderate sized samples Three real datasets Illustrate the methodology (C) 2010 Elsevier B V All rights reserved

Reliability Nonparametric Bayesian Estimation in Parallel Systems

Relevant results for (sub-)distribution functions related to parallel systems are discussed. The reverse hazard rate is defined using the product integral. Consequently, the restriction of absolute continuity for the involved distributions can be relaxed. The only restriction is that the sets of discontinuity points of the parallel distributions have to be disjointed. Nonparametric Bayesian estimators of all survival (sub-)distribution functions are derived. Dual to the series systems that use minimum life times as observations, the parallel systems record the maximum life times. Dirichlet multivariate processes forming a class of prior distributions are considered for the nonparametric Bayesian estimation of the component distribution functions, and the system reliability. For illustration, two striking numerical examples are presented.

The random barrier-crossing problem

This paper addresses the time-variant reliability analysis of structures with random resistance or random system parameters. It deals with the problem of a random load process crossing a random barrier level. The implications of approximating the arrival rate of the first overload by an ensemble-crossing rate are studied. The error involved in this so-called ""ensemble-crossing rate"" approximation is described in terms of load process and barrier distribution parameters, and in terms of the number of load cycles. Existing results are reviewed, and significant improvements involving load process bandwidth, mean-crossing frequency and time are presented. The paper shows that the ensemble-crossing rate approximation can be accurate enough for problems where load process variance is large in comparison to barrier variance, but especially when the number of load cycles is small. This includes important practical applications like random vibration due to impact loadings and earthquake loading. Two application examples are presented, one involving earthquake loading and one involving a frame structure subject to wind and snow loadings. (C) 2007 Elsevier Ltd. All rights reserved.

Quantification of Regional Left and Right Ventricular Deformation Indices in Healthy Neonates by Using Strain Rate and Strain Imaging

Background: Color Doppler myocardial imaging (CDMI) allows the calculation of local longitudinal or radial strain rate (SR) and strain (epsilon). The aims of this study were to determine the feasibility and reproducibility of longitudinal and radial SR and epsilon in neonates during the first hours of life and to establish reference values. Methods: Data were obtained from 55 healthy neonates (29 male; mean age, 20 +/- 14 hours; mean birth weight, 3,174 +/- 374 g). Apical and parasternal views quantified regional longitudinal and radial SR and epsilon in differing ventricular wall segments. Values at peak systole, early diastole, and late diastole were calculated from the extracted curves. CDMI data acquired at 300 +/- 50 frames/s were analyzed offline. Three consecutive cardiac cycles were measured during normal respiration. The timing of specific systolic or diastolic regional events was determined. Multiple comparisons between walls and segments were made. Results: Left ventricular (LV) longitudinal deformation showed basal differences compared with apical segments within one specific wall. Right ventricular (RV) longitudinal deformation was not homogeneous, with significant differences between basal and apical segments. Longitudinal 3 values were higher in the RV free basal and middle wall segments compared with the left ventricle. In the RV free wall apical segment, longitudinal SR and 3 were maximal. LV systolic SR and epsilon values were higher radially compared with longitudinally (radial peak systolic SR midportion, 2.9 +/- 0.6 s(-1); radial peak systolic epsilon 53.8 +/- 19%; longitudinal peak systolic SR midportion, -1.8 +/- 0.5 s(-1); longitudinal peak systolic epsilon, -24.8 +/- 3%; P < .01). Longitudinal systolic epsilon and SR interobserver variability values were 1.2% and 0.7%, respectively. Conclusion: Ultrasound-based SR and 3 imaging is a practical and reproducible clinical technique in neonates, allowing the calculation of regional longitudinal and radial deformation in RV and LV segments. These regional SR and epsilon indices represent new, noninvasive parameters that can quantify normal neonate regional cardiac function. Independent from visual interpretation, they can be used as reference values for diagnosis in ill neonates. (J Am Soc Echocardiogr 2009;22:369-375.)

Influence of Parasympathetic Modulation in Doppler Mitral Inflow Velocity in Individuals without Heart Disease

Background: The relation between left ventricular filing velocities determined by Doppler echocardiography and autonomic nervous system function assessed by heart rate variability (HRV) is unclear. The aim of this study was to evaluate the influence of the autonomic nervous system assessed by the time and frequency domain indices of HRV in the Doppler indices of left ventricular diastolic filling velocities in patients without heart disease. Methods: We studied 451 healthy individuals (255 female [56.4%]) with normal blood pressure, electrocardiogram, chest x-ray, and treadmill electrocardiographic exercise stress test results, with a mean age of 43 +/- 12 (range 15-82) years, who underwent transthoracic Doppler echocardiography and 24-hour electrocardiographic ambulatory monitoring. We studied indices of HRV on time (standard deviation [SD] of all normal sinus RR intervals during 24 hours, SD of averaged normal sinus RR intervals for all 5-minute segments, mean of the SD of all normal sinus RR intervals for all 5-minute segments, root-mean-square of the successive normal sinus RR interval difference, and percentage of successive normal sinus RR intervals > 50 ms) and frequency (low frequency, high frequency, very low frequency, low frequency/high frequency ratio) domains relative to peak flow velocity during rapid passive filling phase (E), atrial contraction (A), E/A ratio, E-wave deceleration time, and isovolumic relaxation time. Statistical analysis was performed with Pearson correlation and logistic regression. Results: Peak flow velocity during rapid passive filling phase (E) and atrial contraction (A), E/A ratio, and deceleration time of early mitral inflow did not demonstrate a significant correlation with indices of HRV in time and frequency domain. We found that the E/A ratio was < 1 in 45 individuals (10%). Individuals with an E/A ratio < 1 had lower indices of HRV in frequency domain (except low frequency/high frequency) and lower indices of the mean of the SD of all normal sinus RR intervals for all 5-minute segments, root-mean-square of the successive normal sinus RR interval difference, and percentage of successive normal sinus RR intervals > 50 ms in time domain. Logistic regression demonstrated that an E/A ratio < 1 was associated with lower HF. Conclusion: Individuals with no evidence of heart disease and an E/A ratio < 1 demonstrated a significant decrease in indexes of HRV associated with parasympathetic modulation. (J Am Soc Echocardiogr 2010;23: 762-5.)

The Poisson-exponential lifetime distribution

In this paper we proposed a new two-parameters lifetime distribution with increasing failure rate. The new distribution arises on a latent complementary risk problem base. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulae for its reliability and failure rate functions, quantiles and moments, including the mean and variance. A simple EM-type algorithm for iteratively computing maximum likelihood estimates is presented. The Fisher information matrix is derived analytically in order to obtaining the asymptotic covariance matrix. The methodology is illustrated on a real data set. (C) 2010 Elsevier B.V. All rights reserved.

The complementary exponential geometric distribution: Model, properties, and a comparison with its counterpart

In this paper, we proposed a new two-parameter lifetime distribution with increasing failure rate, the complementary exponential geometric distribution, which is complementary to the exponential geometric model proposed by Adamidis and Loukas (1998). The new distribution arises on a latent complementary risks scenario, in which the lifetime associated with a particular risk is not observable; rather, we observe only the maximum lifetime value among all risks. The properties of the proposed distribution are discussed, including a formal proof of its probability density function and explicit algebraic formulas for its reliability and failure rate functions, moments, including the mean and variance, variation coefficient, and modal value. The parameter estimation is based on the usual maximum likelihood approach. We report the results of a misspecification simulation study performed in order to assess the extent of misspecification errors when testing the exponential geometric distribution against our complementary one in the presence of different sample size and censoring percentage. The methodology is illustrated on four real datasets; we also make a comparison between both modeling approaches. (C) 2011 Elsevier B.V. All rights reserved.

The Kumaraswamy Weibull distribution with application to failure data

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed. (C) 2010 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

General results for the beta-modified Weibull distribution

We study in detail the so-called beta-modified Weibull distribution, motivated by the wide use of the Weibull distribution in practice, and also for the fact that the generalization provides a continuous crossover towards cases with different shapes. The new distribution is important since it contains as special sub-models some widely-known distributions, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among several others. It also provides more flexibility to analyse complex real data. Various mathematical properties of this distribution are derived, including its moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are also derived for the chf, mean deviations, Bonferroni and Lorenz curves, reliability and entropies. The estimation of parameters is approached by two methods: moments and maximum likelihood. We compare by simulation the performances of the estimates from these methods. We obtain the expected information matrix. Two applications are presented to illustrate the proposed distribution.

The generalized inverse Weibull distribution

The inverse Weibull distribution has the ability to model failure rates which are quite common in reliability and biological studies. A three-parameter generalized inverse Weibull distribution with decreasing and unimodal failure rate is introduced and studied. We provide a comprehensive treatment of the mathematical properties of the new distribution including expressions for the moment generating function and the rth generalized moment. The mixture model of two generalized inverse Weibull distributions is investigated. The identifiability property of the mixture model is demonstrated. For the first time, we propose a location-scale regression model based on the log-generalized inverse Weibull distribution for modeling lifetime data. In addition, we develop some diagnostic tools for sensitivity analysis. Two applications of real data are given to illustrate the potentiality of the proposed regression model.

The beta modified Weibull distribution

A five-parameter distribution so-called the beta modified Weibull distribution is defined and studied. The new distribution contains, as special submodels, several important distributions discussed in the literature, such as the generalized modified Weibull, beta Weibull, exponentiated Weibull, beta exponential, modified Weibull and Weibull distributions, among others. The new distribution can be used effectively in the analysis of survival data since it accommodates monotone, unimodal and bathtub-shaped hazard functions. We derive the moments and examine the order statistics and their moments. We propose the method of maximum likelihood for estimating the model parameters and obtain the observed information matrix. A real data set is used to illustrate the importance and flexibility of the new distribution.

A simple relation between the Leimkuhler curve and the mean residual life

In this paper, a simple relation between the Leimkuhler curve and the mean residual life is established. The result is illustrated with several models commonly used in informetrics, such as exponential, Pareto and lognormal. Finally, relationships with some other reliability concepts are also presented. (C) 2010 Elsevier Ltd. All rights reserved.

Reliability properties under a stopping time shift

Considering a series representation of a coherent system using a shift transform of the components lifetime T-i, at its critical level Y-i, we study two problems. First, under such a shift transform, we analyse the preservation properties of the non-parametric distribution classes and secondly the association preserving property of the components lifetime under such transformations. (c) 2007 Elsevier B.V. All rights reserved.