Aspectos computacionais para inferência na distribuição gama generalizada

Pós-graduação em Matematica Aplicada e Computacional - FCT

An extended Lindley distribution

In this paper we introduce an extension of the Lindley distribution which offers a more flexible model for lifetime data. Several statistical properties of the distribution are explored, such as the density, (reversed) failure rate, (reversed) mean residual lifetime, moments, order statistics, Bonferroni and Lorenz curves. Estimation using the maximum likelihood and inference of a random sample from the distribution are investigated. A real data application illustrates the performance of the distribution. (C) 2011 The Korean Statistical Society. Published by Elsevier B.V. All rights reserved.

The geometric Birnbaum-Saunders regression model with cure rate

In this paper, we propose a cure rate survival model by assuming the number of competing causes of the event of interest follows the Geometric distribution and the time to event follow a Birnbaum Saunders distribution. We consider a frequentist analysis for parameter estimation of a Geometric Birnbaum Saunders model with cure rate. Finally, to analyze a data set from the medical area. (C) 2011 Elsevier B.V. All rights reserved.

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.

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 negative binomial-beta Weibull regression model to predict the cure of prostate cancer

In this article, for the first time, we propose the negative binomial-beta Weibull (BW) regression model for studying the recurrence of prostate cancer and to predict the cure fraction for patients with clinically localized prostate cancer treated by open radical prostatectomy. The cure model considers that a fraction of the survivors are cured of the disease. The survival function for the population of patients can be modeled by a cure parametric model using the BW distribution. We derive an explicit expansion for the moments of the recurrence time distribution for the uncured individuals. The proposed distribution can be used to model survival data when the hazard rate function is increasing, decreasing, unimodal and bathtub shaped. Another advantage is that the proposed model includes as special sub-models some of the well-known cure rate models discussed in the literature. We derive the appropriate matrices for assessing local influence on the parameter estimates under different perturbation schemes. We analyze a real data set for localized prostate cancer patients after open radical prostatectomy.

Data mining for lifetime prediction of metallic components

The ability to accurately predict the lifetime of building components is crucial to optimizing building design, material selection and scheduling of required maintenance. This paper discusses a number of possible data mining methods that can be applied to do the lifetime prediction of metallic components and how different sources of service life information could be integrated to form the basis of the lifetime prediction model

Bounds on the Lifetime of Wireless Sensor Networks Employing Multiple Data Sinks

Employing multiple base stations is an attractive approach to enhance the lifetime of wireless sensor networks. In this paper, we address the fundamental question concerning the limits on the network lifetime in sensor networks when multiple base stations are deployed as data sinks. Specifically, we derive upper bounds on the network lifetime when multiple base stations are employed, and obtain optimum locations of the base stations (BSs) that maximize these lifetime bounds. For the case of two BSs, we jointly optimize the BS locations by maximizing the lifetime bound using a genetic algorithm based optimization. Joint optimization for more number of BSs is complex. Hence, for the case of three BSs, we optimize the third BS location using the previously obtained optimum locations of the first two BSs. We also provide simulation results that validate the lifetime bounds and the optimum locations of the BSs.

Enhancing lifetime of wireless sensor networks using multiple data sinks

In this paper, we address the fundamental question concerning the limits on the network lifetime in sensor networks when multiple base stations (BSs) are deployed as data sinks. Specifically, we derive upper bounds on the network lifetime when multiple BSs arc employed, and obtain optimum locations of the base stations that maximise these lifetime bounds. For the case of two BSs, we jointly optimise the BS locations by maximising the lifetime bound using genetic algorithm. Joint optimisation for more number of BSs becomes prohibitively complex. Further, we propose a suboptimal approach for higher number of BSs, Individually Optimum method, where we optimise the next BS location using optimum location of previous BSs. Individually Optimum method has advantage of being attractive for solving the problem with more number of BSs at the cost of little compromised accuracy. We show that accuracy degradation is quite small for the case of three BSs.

Inference for the Component and System Lifetime Distribution of a k-unit Parallel System Based on System Data

In this paper, we consider the inference for the component and system lifetime distribution of a k-unit parallel system with independent components based on system data. The components are assumed to have identical Weibull distribution. We obtain the maximum likelihood estimates of the unknown parameters based on system data. The Fisher information matrix has been derived. We propose -expectation tolerance interval and -content -level tolerance interval for the life distribution of the system. Performance of the estimators and tolerance intervals is investigated via simulation study. A simulated dataset is analyzed for illustration.

Standardization of data collection for the Lifetime Surveillance of Astronaut Health (LSAH)

Problems due to the lack of data standardization and data management have lead to work inefficiencies for the staff working with the vision data for the Lifetime Surveillance of Astronaut Health. Data has been collected over 50 years in a variety of manners and then entered into a software. The lack of communication between the electronic health record (EHR) form designer, epidemiologists, and optometrists has led to some level to confusion on the capability of the EHR system and how its forms can be designed to fit all the needs of the relevant parties. EHR form customizations or form redesigns were found to be critical for using NASA's EHR system in the most beneficial way for its patients, optometrists, and epidemiologists. In order to implement a protocol, data being collected was examined to find the differences in data collection methods. Changes were implemented through the establishment of a process improvement team (PIT). Based on the findings of the PIT, suggestions have been made to improve the current EHR system. If the suggestions are implemented correctly, this will not only improve efficiency of the staff at NASA and its contractors, but set guidelines for changes in other forms such as the vision exam forms. Because NASA is at the forefront of such research and health surveillance the impact of this management change could have a drastic improvement on the collection of and adaptability of the EHR. Accurate data collection from this 50+ year study is ongoing and is going to help current and future generations understand the implications of space flight on human health. It is imperative that the vast amount of information is documented correctly.^

The user query based learning system for lifetime prediction of metallic components

Real-World Data Mining Applications generally do not end up with the creation of the models. The use of the model is the final purpose especially in prediction tasks. The problem arises when the model is built based on much more information than that the user can provide in using the model. As a result, the performance of model reduces drastically due to many missing attributes values. This paper develops a new learning system framework, called as User Query Based Learning System (UQBLS), for building data mining models best suitable for users use. We demonstrate its deployment in a real-world application of the lifetime prediction of metallic components in buildings

Component reliability estimations without field data

Maintenance activities in a large-scale engineering system are usually scheduled according to the lifetimes of various components in order to ensure the overall reliability of the system. Lifetimes of components can be deduced by the corresponding probability distributions with parameters estimated from past failure data. While failure data of the components is not always readily available, the engineers have to be content with the primitive information from the manufacturers only, such as the mean and standard deviation of lifetime, to plan for the maintenance activities. In this paper, the moment-based piecewise polynomial model (MPPM) are proposed to estimate the parameters of the reliability probability distribution of the products when only the mean and standard deviation of the product lifetime are known. This method employs a group of polynomial functions to estimate the two parameters of the Weibull Distribution according to the mathematical relationship between the shape parameter of two-parameters Weibull Distribution and the ratio of mean and standard deviation. Tests are carried out to evaluate the validity and accuracy of the proposed methods with discussions on its suitability of applications. The proposed method is particularly useful for reliability-critical systems, such as railway and power systems, in which the maintenance activities are scheduled according to the expected lifetimes of the system components.

The economics of happiness : a lifetime perspective

The three studies in this thesis focus on happiness and age and seek to contribute to our understanding of happiness change over the lifetime. The first study contributes by offering an explanation for what was evolving to a ‘stylised fact’ in the economics literature, the U-shape of happiness in age. No U-shape is evident if one makes a visual inspection of the age happiness relationship in the German socio-economic panel data, and, it seems counter-intuitive that we just have to wait until we get old to be happy. Eliminating the very young, the very old, and the first timers from the analysis did not explain away regression results supporting the U-shape of happiness in age, but fixed effect analysis did. Analysis revealed found that reverse causality arising from time-invariant individual traits explained the U-shape of happiness in age in the German population, and the results were robust across six econometric methods. Robustness was added to the German fixed effect finding by replicating it with the Australian and the British socio-economic panel data sets. During analysis of the German data an unexpected finding emerged, an exceedingly large negative linear effect of age on happiness in fixed-effect regressions. There is a large self-reported happiness decline by those who remain in the German panel. A similar decline over time was not evident in the Australian or the British data. After testing away age, time and cohort effects, a time-in-panel effect was found. Germans who remain in the panel for longer progressively report lower levels of happiness. Because time-in-panel effects have not been included in happiness regression specifications, our estimates may be biased; perhaps some economics of the happiness studies, that used German panel data, need revisiting. The second study builds upon the fixed-effect finding of the first study and extends our view of lifetime happiness to a cohort little visited by economists, children. Initial analysis extends our view of lifetime happiness beyond adulthood and revealed a happiness decline in adolescent (15 to 23 year-old) Australians that is twice the size of the happiness decline we see in older Australians (75 to 86 yearolds), who we expect to be unhappy due to declining income, failing health and the onset of death. To resolve a difference of opinion in the literature as to whether childhood happiness decreases, increases, or remains flat in age; survey instruments and an Internet-based survey were developed and used to collect data from four hundred 9 to 14 year-old Australian children. Applying the data to a Model of Childhood Happiness revealed that the natural environment life-satisfaction domain factor did not have a significant effect on childhood happiness. However, the children’s school environment and interactions with friends life-satisfaction domain factors explained over half a steep decline in childhood happiness that is three times larger than what we see in older Australians. Adding personality to the model revealed what we expect to see with adults, extraverted children are happier, but unexpectedly, so are conscientious children. With the steep decline in the happiness of young Australians revealed and explanations offered, the third study builds on the time-invariant individual trait finding from the first study by applying the Australian panel data to an Aggregate Model of Average Happiness over the lifetime. The model’s independent variable is the stress that arises from the interaction between personality and the life event shocks that affect individuals and peers throughout their lives. Interestingly, a graphic depiction of the stress in age relationship reveals an inverse U-shape; an inverse U-shape that looks like the opposite of the U-shape of happiness in age we saw in the first study. The stress arising from life event shocks is found to explain much of the change in average happiness over a lifetime. With the policy recommendations of economists potentially invoking unexpected changes in our lives, the ensuing stress and resulting (un)happiness warrant consideration before economists make policy recommendations.