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Title: A new cut-point PH-distribution to fit a Survival data set Authors:  Juan Eloy Ruiz-Castro - University of Granada (Spain)
Christian Acal - University of Granada (Spain) [presenting]
Abstract: Phase-type distributions (PHD) are a suitable candidate to model complex problems in an algorithmic and computational way. Among other properties, PHD class stands out for being dense in the set of probability distributions on the non-negative half-line, which enables to approximate as much as desired any non-negative probability distribution. Nevertheless, the drawback is that the estimation of the PHD parameters is not a simple task since the PHD representation is not unique. Although the fitting is really acceptable on most occasions, two aspects raise some concern in the optimization problem: the number of parameters to be estimated is usually high, and at times PHDs do not provide good results in the tails of the distribution. A novel methodology based on PH distributions with multiple cut-points is proposed. In particular, a new distribution called multiple cut-points PHD is introduced to solve the lack of power in the distribution tails and to reduce the number of parameters in the estimation. This class of distributions is studied in detail and several associated measures are worked out. An EM algorithm is developed for parameter estimation. The results have been implemented in R-cran and multiple examples are developed.