The Conway-Maxwell-Poisson-generalized gamma regression model with long-term survivors

In this paper, we proposed a flexible cure rate survival model by assuming the number of competing causes of the event of interest following the Conway-Maxwell distribution and the time for the event to follow the generalized gamma distribution. This distribution can be used to model survival data when the hazard rate function is increasing, decreasing, bathtub and unimodal-shaped including some distributions commonly used in lifetime analysis as particular cases. Some appropriate matrices are derived in order to evaluate local influence on the estimates of the parameters by considering different perturbations, and some global influence measurements are also investigated. Finally, data set from the medical area is analysed.

The log-exponentiated generalized gamma regression model for censored data

For the first time, we introduce a generalized form of the exponentiated generalized gamma distribution [Cordeiro et al. The exponentiated generalized gamma distribution with application to lifetime data, J. Statist. Comput. Simul. 81 (2011), pp. 827-842.] that is the baseline for the log-exponentiated generalized gamma regression model. The new distribution can accommodate increasing, decreasing, bathtub- and unimodal-shaped hazard functions. A second advantage is that it includes classical distributions reported in the lifetime literature as special cases. We obtain explicit expressions for the moments of the baseline distribution of the new regression model. The proposed model can be applied to censored data since it includes as sub-models several widely known regression models. It therefore can be used more effectively in the analysis of survival data. We obtain maximum likelihood estimates for the model parameters by considering censored data. We show that our extended regression model is very useful by means of two applications to real data.

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 Bayesian Analysis in the Presence of Covariates for Multivariate Survival Data: An example of Application

In this paper, we introduce a Bayesian analysis for survival multivariate data in the presence of a covariate vector and censored observations. Different ""frailties"" or latent variables are considered to capture the correlation among the survival times for the same individual. We assume Weibull or generalized Gamma distributions considering right censored lifetime data. We develop the Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods.

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.

Robust Bayesian analysis of heavy-tailed stochastic volatility models using scale mixtures of normal distributions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Aspectos computacionais para inferência na distribuição gama generalizada

Pós-graduação em Matematica Aplicada e Computacional - FCT

The impact of asymptomatic vertebral fractures on quality of life in older community-dwelling women: the Sao Paulo Ageing & Health Study

OBJECTIVES: The aim of this study was to investigate the impact of asymptomatic vertebral fractures on the quality of life in older women as part of the Sao Paulo Ageing & Health Study. METHODS: This study was a cross-sectional study with a random sample of 180 women 65 years of age or older with or without vertebral fractures. The Quality of Life Questionnaire of the European Foundation for Osteoporosis was administered to all subjects. Anthropometric data were obtained by physical examination, and the body mass index was calculated. Lateral thoracic and lumbar spine X-ray scans were obtained to identify asymptomatic vertebral fractures using a semi-quantitative method. RESULTS: Women with asymptomatic vertebral fractures had lower total scores [61.4(15.3) vs. 67.1(14.2), p = 0.03] and worse physical function domain scores [69.5(20.1) vs. 77.3(17.1), p = 0.02] for the Quality of Life Questionnaire of the European Foundation for Osteoporosis compared with women without fractures. The total score of this questionnaire was also worse in women classified as obese than in women classified as overweight or normal. High physical activity was related to a better total score for this questionnaire (p = 0.01). Likewise, lower physical function scores were observed in women with higher body mass index values (p < 0.05) and lower physical activity levels (p < 0.05). Generalized linear models with gamma distributions and logarithmic link functions, adjusted for age, showed that lower total scores and physical function domain scores for the Quality of Life Questionnaire of the European Foundation for Osteoporosis were related to a high body mass index, lower physical activity, and the presence of vertebral fractures (p < 0.05). CONCLUSION: Vertebral fractures are associated with decreased quality of life mainly physical functioning in older community-dwelling women regardless of age, body mass index, and physical activity. Therefore, the results highlight the importance of preventing and controlling asymptomatic vertebral fractures to reduce their impact on quality of life among older women.

The impact of asymptomatic vertebral fractures on quality of life in older community-dwelling women: the São Paulo Ageing & Health Study

OBJECTIVES: The aim of this study was to investigate the impact of asymptomatic vertebral fractures on the quality of life in older women as part of the Sao Paulo Ageing & Health Study. METHODS: This study was a cross-sectional study with a random sample of 180 women 65 years of age or older with or without vertebral fractures. The Quality of Life Questionnaire of the European Foundation for Osteoporosis was administered to all subjects. Anthropometric data were obtained by physical examination, and the body mass index was calculated. Lateral thoracic and lumbar spine X-ray scans were obtained to identify asymptomatic vertebral fractures using a semi-quantitative method. RESULTS: Women with asymptomatic vertebral fractures had lower total scores [61.4(15.3) vs. 67.1(14.2), p = 0.03] and worse physical function domain scores [69.5(20.1) vs. 77.3(17.1), p = 0.02] for the Quality of Life Questionnaire of the European Foundation for Osteoporosis compared with women without fractures. The total score of this questionnaire was also worse in women classified as obese than in women classified as overweight or normal. High physical activity was related to a better total score for this questionnaire (p = 0.01). Likewise, lower physical function scores were observed in women with higher body mass index values (p<0.05) and lower physical activity levels (p,0.05). Generalized linear models with gamma distributions and logarithmic link functions, adjusted for age, showed that lower total scores and physical function domain scores for the Quality of Life Questionnaire of the European Foundation for Osteoporosis were related to a high body mass index, lower physical activity, and the presence of vertebral fractures (p<0.05). CONCLUSION: Vertebral fractures are associated with decreased quality of life mainly physical functioning in older community-dwelling women regardless of age, body mass index, and physical activity. Therefore, the results highlight the importance of preventing and controlling asymptomatic vertebral fractures to reduce their impact on quality of life among older women.

Empirical Analysis of Credit Risk Regime Switching and Temporal Conditional Default Correlation in Credit Default Swap Valuation: The Market liquidity effect

In this paper, we extend the debate concerning Credit Default Swap valuation to include time varying correlation and co-variances. Traditional multi-variate techniques treat the correlations between covariates as constant over time; however, this view is not supported by the data. Secondly, since financial data does not follow a normal distribution because of its heavy tails, modeling the data using a Generalized Linear model (GLM) incorporating copulas emerge as a more robust technique over traditional approaches. This paper also includes an empirical analysis of the regime switching dynamics of credit risk in the presence of liquidity by following the general practice of assuming that credit and market risk follow a Markov process. The study was based on Credit Default Swap data obtained from Bloomberg that spanned the period January 1st 2004 to August 08th 2006. The empirical examination of the regime switching tendencies provided quantitative support to the anecdotal view that liquidity decreases as credit quality deteriorates. The analysis also examined the joint probability distribution of the credit risk determinants across credit quality through the use of a copula function which disaggregates the behavior embedded in the marginal gamma distributions, so as to isolate the level of dependence which is captured in the copula function. The results suggest that the time varying joint correlation matrix performed far superior as compared to the constant correlation matrix; the centerpiece of linear regression models.

Information Matrix for Beta Distributions

2000 Mathematics Subject Classification: 33C90, 62E99.

Vesicle motion during sustained exocytosis in chromaffin cells

Chromaffin cells release catecholamines by exocytosis, a process that includes vesicle docking, priming and fusion. Although all these steps have been intensively studied, some aspects of their mechanisms, particularly those regarding vesicle transport to the active sites situated at the membrane, are still unclear. In this work, we show that it is possible to extract information on vesicle motion in Chromaffin cells from the combination of Langevin simulations and amperometric measurements. We developed a numerical model based on Langevin simulations of vesicle motion towards the cell membrane and on the statistical analysis of vesicle arrival times. We also performed amperometric experiments in bovine-adrenal Chromaffin cells under Ba2+ stimulation to capture neurotransmitter releases during sustained exocytosis. In the sustained phase, each amperometric peak can be related to a single release from a new vesicle arriving at the active site. The amperometric signal can then be mapped into a spike-series of release events. We normalized the spike-series resulting from the current peaks using a time-rescaling transformation, thus making signals coming from different cells comparable. We discuss why the obtained spike-series may contain information about the motion of all vesicles leading to release of catecholamines. We show that the release statistics in our experiments considerably deviate from Poisson processes. Moreover, the interspike-time probability is reasonably well described by two-parameter gamma distributions. In order to interpret this result we computed the vesicles’ arrival statistics from our Langevin simulations. As expected, assuming purely diffusive vesicle motion we obtain Poisson statistics. However, if we assume that all vesicles are guided toward the membrane by an attractive harmonic potential, simulations also lead to gamma distributions of the interspike-time probability, in remarkably good agreement with experiment. We also show that including the fusion-time statistics in our model does not produce any significant changes on the results. These findings indicate that the motion of the whole ensemble of vesicles towards the membrane is directed and reflected in the amperometric signals. Our results confirm the conclusions of previous imaging studies performed on single vesicles that vesicles’ motion underneath plasma membranes is not purely random, but biased towards the membrane.