In this work, expressions of the cumulative distribution function of Y X, Y/X and X/(X + Y ) for continuous dependent random variables with supported on a unbounded and bounded interval are derived. The dependence approach is based on copula functions. Additionally, the methodology is applied to real data on hydrology.

In this work, expressions of the cumulative distribution function of Y X, Y/X and X/(X + Y ) for continuous dependent random variables with supported on a unbounded and bounded interval are derived. The dependence approach is based on copula functions. Additionally, the methodology is applied to real data on hydrology.

This paper presents a regression model for discrete time data with cure fraction. For this purpose, we considered a mixture model, in which times are modeled through the discrete Weibull distribution and the cure probability modeled with covariates by using the logit link function. Considering that the model is a mixture, the estimation of the parameters was performed by EM algorithm. The behavior of the estimating algorithm was tested with Monte Carlo simulation experiments and an application for real data was added.

This paper presents a regression model for discrete time data with cure fraction. For this purpose, we considered a mixture model, in which times are modeled through the discrete Weibull distribution and the cure probability modeled with covariates by using the logit link function. Considering that the model is a mixture, the estimation of the parameters was performed by EM algorithm. The behavior of the estimating algorithm was tested with Monte Carlo simulation experiments and an application for real data was added.

In a ARMA-APARCH time series model with innovations Z, the delta-stationarity condition of the APARCH process involves the delta-th moment of the difference between the absolute value of the innovations with the product of the asymmetry parameter and the innovations. This moment allows calculating more efficiently the estimates of the parameters of the model by maximum likelihood. In this article, we obtain explicit expressions of this delta - th moment where Z has stable and GEV distribution. These moments have been implemented in our GEVStableGarch package available in CRAN R-PROJECT developed to estimate the parameters of ARMA-GARCH / APARCH models with stable innovations and GEV.

In a ARMA-APARCH time series model with innovations Z, the delta-stationarity condition of the APARCH process involves the delta-th moment of the difference between the absolute value of the innovations with the product of the asymmetry parameter and the innovations. This moment allows calculating more efficiently the estimates of the parameters of the model by maximum likelihood. In this article, we obtain explicit expressions of this delta - th moment where Z has stable and GEV distribution. These moments have been implemented in our GEVStableGarch package available in CRAN R-PROJECT developed to estimate the parameters of ARMA-GARCH / APARCH models with stable innovations and GEV.