Abstract:

Nowadays statistics is highly present in any branch of the science. Knowing and handling properly the main statistical tools is almost a required assignment for any worker who deals with numbers during their professional career. For this reason, the most of Spanish University Degrees have (at least) a compulsory course related to statistics in their educational programme. Among the challenges facing university teaching, there is a clear consensus on adapting learning methodologies in statistics to the new educative systems that are emerging from last decades thanks to the computational development that the sector is undergoing. Many applications are being developed so that students have tutorial videos, self-readable theoretical part, guiding exercises, etc. in a few clicks. However, most of these apps are focused on very general concepts (descriptive statistic, regression, correlation or classical probability distributions). Therefore, there is a great need to develop tools that address more complex statistical techniques. In this respect, a new methodology for the teaching and learning of phase-type distributions (PHD) is introduced in this work. PHD are widely used in the reliability sector to model the lifetime of any system. This novel methodology is based on the Shiny package, which makes easier the creation of interactive web applications through the statistical software R. With the support of this passage, the behaviour of a PHD with multiple structures such as exponential distribution, Erlang distribution or Coxian distribution, among others, is analysed. The estimation of different phase-type structures for a dataset is also presented in an interactive way by considering several estimation methodologies available in the Mapfit package from R. The developed study allows to simultaneously compare the graphic fit of different PHD, as well as the estimation of its parameters and analyze the goodness of the fit. The methodology carried out has also made it possible to extend the teaching/learning process of complex statistics problems. Thus, it has also been extended for the case of one cut-point PHD.

Keywords:

Phase-type distributions, teaching, shiny, R-cran.