Adriano K. Suzuki

The Long-Term Bivariate Survival FGM Copula Model: An Application to a Brazilian HIV Data

In this paper we propose a new bivariate long-term distribu- tion based on the Farlie-Gumbel-Morgenstern copula model. The proposed model allows for the presence of censored data and covariates in the cure parameter. For inferential purpose a Bayesian approach via Markov Chain Monte Carlo (MCMC) is considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and inuential ob- servations, we develop a Bayesian case deletion inuence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated on articial and real HIV data.

The FGM Long-Term Bivariate Survival Copula Model: Modeling, Bayesian Estimation, and Case Influence Diagnostics

In this article, we propose a bivariate long-term distribution based on the Farlie-Gumbel-Morgenstern copula model. The proposed model allows for the presence of censored data and covariates. For inferential purposes, a Bayesian approach via Markov Chain Monte Carlo (MCMC) were considered. Further, some discussions on the model selection criteria are given. In order to examine outlying and influential observations, we present a Bayesian case deletion influence diagnostics based on the Kullback-Leibler divergence. The newly developed procedures are illustrated on artificial and real data.

A non-default fraction bivariate regression model for credit scoring: An application to Brazilian customer data

ABSTRACT In this article, we propose a lifetime model for bivariate survival data with a non-default rate. Our approach enables different underlying activation mechanisms that lead to the event of interest. A number of competing causes which may be responsible for the occurrence of the event of interest are assumed to follow a Poisson distributions, and a positive stable distribution was considered for the frailty component. The Markov chain Monte Carlo (MCMC) method is used in Bayesian inference approach and some Bayesian criteria are used for a comparison. Moreover, we conduct the influence diagnostic through the diagnostic measures in order to detect possible influential or extreme observations that can cause distortions on the results of the analysis. The proposed models are applied to analyze a Brazilian customer data set.

The odd Lomax generator of distributions: Properties, estimation and applications

Abstract We introduce a new family of continuous distributions called the odd Lomax-G class and provide four special models. We derive explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, order statistics and probability weighted moments. The maximum likelihood and least squares methods are used to estimate the model parameters. The flexibility of the proposed family is illustrated by means of two applications to real data sets.

Bayesian computational methods for sampling from the posterior distribution of a bivariate survival model, based on AMH copula in the presence of right-censored data

In this paper, we study the performance of Bayesian computational methods to estimate the parameters of a bivariate survival model based on the Ali–Mikhail–Haq copula with marginal distributions given by Weibull distributions. The estimation procedure was based on Monte Carlo Markov Chain (MCMC) algorithms. We present three version of the Metropolis–Hastings algorithm: Independent Metropolis–Hastings (IMH), Random Walk Metropolis (RWM) and Metropolis–Hastings with a natural-candidate generating density (MH). Since the creation of a good candidate generating density in IMH and RWM may be difficult, we also describe how to update a parameter of interest using the slice sampling (SS) method. A simulation study was carried out to compare the performances of the IMH, RWM and SS. A comparison was made using the sample root mean square error as an indicator of performance. Results obtained from the simulations show that the SS algorithm is an effective alternative to the IMH and RWM methods when simulating values from the posterior distribution, especially for small sample sizes. We also applied these methods to a real data set.

A new destructive Poisson odd log-logistic generalized half-normal cure rate model

ABSTRACT We propose a new cure rate survival model by assuming that the initial number of competing causes of the event of interest follows a Poisson distribution and the time to event has the odd log-logistic generalized half-normal distribution. This survival model describes a realistic interpretation for the biological mechanism of the event of interest. We estimate the model parameters using maximum likelihood. For different sample sizes, various simulation scenarios are performed. We propose the diagnostics and residual analysis to verify the model assumptions. The potentiality of the new cure rate model is illustrated by means of a real data.

A general long-term aging model with different underlying activation mechanisms: Modeling, Bayesian estimation, and case influence diagnostics

ABSTRACT In this paper we propose a general cure rate aging model. Our approach enables different underlying activation mechanisms which lead to the event of interest. The number of competing causes of the event of interest is assumed to follow a logarithmic distribution. The model is parameterized in terms of the cured fraction which is then linked to covariates. We explore the use of Markov chain Monte Carlo methods to develop a Bayesian analysis for the proposed model. Moreover, some discussions on the model selection to compare the fitted models are given, as well as case deletion influence diagnostics are developed for the joint posterior distribution based on the ψ-divergence, which has several divergence measures as particular cases, such as the Kullback–Leibler (K-L), J-distance, L1 norm, and χ2-square divergence measures. Simulation studies are performed and experimental results are illustrated based on a real malignant melanoma data.

Cure rate proportional odds models with spatial frailties for interval-censored data

This paper presents proportional odds cure models to allow spatial correlations by including spatial frailty in the interval censored data setting. Parametric cure rate models with independent and dependent spatial frailties are proposed and compared. Our approach enables different underlying activation mechanisms that lead to the event of interest; in addition, the number of competing causes which may be responsible for the occurrence of the event of interest follows a Geometric distribution. Markov chain Monte Carlo method is used in a Bayesian framework for inferential purposes. For model comparison some Bayesian criteria were used. An influence diagnostic analysis was conducted to detect possible influential or extreme observations that may cause distortions on the results of the analysis. Finally, the proposed models are applied for the analysis of a real data set on smoking cessation. The results of the application show that the parametric cure model with frailties under the first activation scheme has better findings.

The Odd Log-Logistic Generalized Gamma Model: Properties, Applications, Classical And Bayesian Approach

The statistics literature is filled with hundreds of continuous univariate distributions. Recent developments focus on new techniques for building meaningful models. More recently, seve ral methods of introducing one or more parameters to generate new distributions have been proposed. Among these methods, the compounding of some discrete and important lifetime distributions has been in the vanguard of lifetime modeling. So, several families of distributions were investigated by compounding some useful lifetime and truncated discrete distributions. The log-logistic (LL) distribution with a shape parameter 0 λ > is a useful model for survival analysis and it is an alternative to the log-normal distribution. Unlike the more commonly used Weibull distribution, the LL distribution has a non-monotonic hazard rate function (hrf), which makes it suitable for modeling cancer survival data. For 1 λ > , the hrf is unimodal and when 1 λ = , the hazard decreases monotonically. The fact that its cumulative distribution function (cdf) has a closed-form is particularly useful for analysis of survival data with censoring.

A Bayesian Approach to Predicting Football Match Outcomes Considering Time Effect Weight

In this chapter we propose a simulation-based method for predicting football match outcomes. We adopt a Bayesian perspective, modeling the number of goals of two opposing teams as a Poisson distribution whose mean is proportional to the relative technical level of opponents. Federation Internationale de Football Association (FIFA) ratings were taken as the measure of technical level of teams saw well as experts’ opinions on the scores of the matches were taken in account to construct the prior distributions of the parameters. Tournament simulations were performed in order to estimate probabilities of winning the tournament assuming different values for the weight attached to the experts’ information and different choices for the sequence of weights attached to the previous observed matches. The methodology is illustrated on the 2010 Football Word Cup.