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In this work, we extend standard likelihood-based procedures to the multivariate linear model using the scale mixtures of multivariate skew-normal-Cauchy distributions. A simple EM algorithm for it...

In recent years, a variety of regression models, including zero-inflated and hurdle versions, have been proposed to explain the case of a dependent variable with respect to exogenous covariates. Apart from the classical Poisson, negative binomial and generalised Poisson distributions, many proposals have appeared in the statistical literature, perhaps in response to the new possibilities offered by advanced software that now enables researchers to implement numerous special functions in a relatively simple way. However, we believe that a significant research gap remains, since very little attention has been paid to the quasi-binomial distribution, which was first proposed over fifty years ago. We believe this distribution might constitute a valid alternative to existing regression models, in situations in which the variable has bounded support. Therefore, in this paper we present a zero-inflated regression model based on the quasi-binomial distribution, taking into account the moments and maximum likelihood estimators, and perform a score test to compare the zero-inflated quasi-binomial distribution with the zero-inflated binomial distribution, and the zero-inflated model with the homogeneous model (the model in which covariates are not considered). This analysis is illustrated with two data sets that are well known in the statistical literature and which contain a large number of zeros.

In this paper, we consider a generalization of the modified slash distribution. We define the new family through the quotient between an elliptically distributed random variable and the power of an exponential random variable with parameter equals to 2, both independent. We use the same idea to extend the model for the multivariate case and study general important properties from the resultant family. We perform inference by the method of moments and maximum likelihood. We present a simulation study which indicates satisfactory parameter recovery by using the estimation approaches. Illustrations reveals that it has potential for doing well in real problems.

In this paper, the Rayleigh–Lindley (RL) distribution is introduced, obtained by compounding the Rayleigh and Lindley discrete distributions, where the compounding procedure follows an approach sim...

Models for dealing with survival data in the presence of a cured fraction of individuals have attracted the attention of many researchers and practitioners in recent years. In this paper, we propos...

In this paper an extension of the piecewise exponential distribution based on the distribution of the maximum of a random sample is considered. Properties of its density and hazard function are investigated. Maximum likelihood inference is discussed and the Fisher information matrix is identified. Results of two real data applications are reported, where model fitting is implemented by using maximum likelihood. The applications illustrate the better performance of the new distribution when compared with other recently proposed alternative models.

To test for differences in cardiovascular and metabolic risk (CMR) by educational attainment and physical capital. To compare CMR among black, indigenous, and mixed populations, accounting for socioeconomic status (SES).We conducted multivariate analyses using cross-sectional data from a national survey of Colombian adults (n = 10,814) to examine the social patterning of CMR. In sex/gender-stratified models, a CMR index was regressed on educational attainment, physical capital, ethnicity/race, and age.Women with a primary education (OR = 1.64, 95% CI: 1.25, 2.15) had higher age- and ethnicity/race-adjusted odds of CMR than women with more than secondary education. Men with a primary education (OR = 0.67, 95% CI: 0.48, 0.92) had significantly lower adjusted odds of CMR than men with more than secondary education; these associations did not remain significant after adjustments for physical capital. Men in the first (OR = 0.45, 95% CI: 0.36, 0.57) and second (OR = 0.72, 95% CI: 0.57, 0.91) physical capital tertiles had significantly lower adjusted odds of CMR than those in the highest tertile. There was not a significant patterning of CMR by ethnicity/race for women or men, or by physical capital for women.Findings suggest that for Colombian adults CMR is patterned by SES; these associations differ by sex/gender.

The family of power series cure rate models provides a flexible modeling framework for survival data of populations with a cure fraction. In this work, we present a simplified estimation procedure for the maximum likelihood (ML) approach. ML estimates are obtained via the expectation-maximization (EM) algorithm where the expectation step involves computation of the expected number of concurrent causes for each individual. It has the big advantage that the maximization step can be decomposed into separate maximizations of two lower-dimensional functions of the regression and survival distribution parameters, respectively. Two simulation studies are performed: the first to investigate the accuracy of the estimation procedure for different numbers of covariates and the second to compare our proposal with the direct maximization of the observed log-likelihood function. Finally, we illustrate the technique for parameter estimation on a dataset of survival times for patients with malignant melanoma.

In this article, we consider the inclusion of random effects in both the survival function for at-risk subjects and the cure probability assuming a bivariate normal distribution for those effects in each cluster. For parameter estimation, we implemented the restricted maximum likelihood (REML) approach. We consider Weibull and Piecewise Exponential distributions to model the survival function for non-cured individuals. Simulation studies are performed, and based on a real database we evaluate the performance of our proposed model. Effect of different follow-up times and the effect of considering independent random effects instead of bivariate random effects are also studied.

In this paper, an algorithm is developed to compute estimates for parameters in destructive weighted Poisson cure rate models. It is shown, analytically, the robustness of the procedure with respect to the maximization of the observed likelihood function. The approach allows a simple implementation of different distributions for non-destroyed concurrent causes. The performance of the method is evaluated through simulation studies and by analysing a real data set related to patients with malignant melanoma.