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Bandt and Pompe introduced Permutation Entropy in 2002 for Time Series whereequal values, xt1 = xt2, t1 = t2, were neglected and only inequalities betweenthe xt were considered. Since then, this measure has been modified andextended, in particular in cases when the amount of equal values in the seriescan not be neglected, (i.e. heart rate variability (HRV) time series). Wereview the different existing methodologies that treats this subject byclassifying them according to their different strategies. In addition, a novelBayesian Missing Data Imputation is presented that proves to outperform theexisting methodologies that deals with type of time series. All this facts areillustrated by simulations and also by distinguishing patients suffering fromCongestive Heart Failure from a (healthy) control group using HRV time series

An empirical evaluation of alternative methods of estimation for Permutation Entropy in time series with tied values