Distributional modelling of positively skewed data via the flexible Weibull extension distribution

The time until an event occurs is often known to have a skewed distribution. To model this, a statistical distribution called the two-parameter flexible Weibull extension (FWE) has been proposed. In this paper, the FWE distribution is used to model datasets through the use of generalised additive models for location, scale and shape (GAMLSS) distributional regression. GAMLSS is the only regression technique that can examine the effects of both categorical and numeric predictors on all the parameters of the distribution used to fit the dependent variable. To make it easier to use the FWE distribution through GAMLSS, the RelDists R package is proposed. A simulation study shows that FWE modelling through GAMLSS provides reliable parameter estimates even in the presence of factors that affect the distribution.