Abstract: In this paper we introduce bivariate Weibull distributions derived from copula functions in presence of cure fraction, censored data and covariates. Two copla functions are explored: the FGM (Farlie - Gumbel Morgenstern) copula and the Gumbel copula. Inferences for the proposed models are obtained under the Bayesian approach, using standard MCMC (Markov Chain Monte Carlo) methods. An illustration of the proposed methodology is given considering a medical data set.
In this study we have considered different methods of estimation of the unknown parameters of a two-parameter unit-Gamma (UG) distribution from the frequentists point of view. First, we briefly describe different frequentists approaches: maximum likelihood estimators, moments estimators, least squares estimators, maximum product of spacings estimators, method of Cramer-von-Mises, methods of AndersonDarling and four variants of Anderson-Darling test and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The performances of the estimators have been compared in terms of their bias and root mean squared error using simulated samples. Also, for each method of estimation, we consider the interval estimation using the bootstrap method and calculate the coverage probability and the average width of the bootstrap confidence intervals. The study reveals that the maximum product of spacing estimators and Anderson-Darling 2 (AD2) estimators are highly competitive with the maximum likelihood estimators in small and large samples. Finally, two real data sets have been analyzed for illustrative purposes.
Although the two-parameter Beta distribution is the standard distribution for
analyzing data in the unit interval, there are in the literature some useful and interesting alternatives which are often under-used. An example is the two parameter complementary Beta distribution, introduced by Jones (2002) and, to the best of our knowledge, used only by Iacobellis (2008) as a probabilistic model for the estimation of T year flow duration curves. In his paper the parameters of complementary Beta distribution were successfully estimated, perhaps due to its simplicity, by means of the L-moments method. The objective of this paper is to compare, using Monte Carlo simulations, the bias and mean-squared error, of the estimators obtained by the methods of L-moments and maximum likelihood. The simulation study showed that the maximum likelihood method has bias and mean -squared error lower than L-moments. It is also revealed that the parameters estimated by the maximum likelihood are negatively biased, while by the L-moments method the parameters are positively biased. Data on relative indices from annual temperature extremes (percentage of cool nights, percentage of warm nights, percentage of cool days and percentage of warm days) in Uruguay are used for illustrative purposes.
One of the key features in regression models consists in selecting appropriate characteristics that explain the behavior of the response variable, in which stepwise-based procedures occupy a prominent position. In this paper we performed several simulation studies to investigate whether a specific stepwise-based approach, namely Strategy A, properly selects authentic variables into the generalized additive models for location, scale and shape framework, considering Gaussian, zero inflated Poisson and Weibull distributions. Continuous (with linear and nonlinear relationships) and categorical explanatory variables are considered and they are selected through some goodness-of-fit statistics. Overall, we conclude that the Strategy A greatly performed.