Fetal heart rate discrimination is an evolving field in biomedical engineering with many efforts dedicated to avoid preterm deliveries by way of improving fetus monitoring methods and devices. Entropy analysis is a nonlinear signal analysis technique that has been progressively developed to improve the discriminability of a several physiological signals, with Kernel based entropy parameters (KBEPs) found advantageous over standard techniques. This study is the first to apply KBEPs to analyze fetal heart rates. Specifically, it explores the usability of the cutting-edge nonlinear KBEPs in discriminating between healthy fetuses and fetuses under distress. The database used in this study comprises 50 healthy and 50 distressed fetal heart rate signals with severe intrauterine growth restriction. The Cascade analysis investigates six kernel based entropy measures on fetal heart rates discrimination, and compares them to four standard entropies. The study presents a statistical evaluation of the discrimination power of each parameter (paired t-test statistics and distribution spread). Simulation results showed that the distribution ranges in 80% of the entropy parameters in the distressed heart group are higher than those in the healthy control group. Moreover, the results show that it is advantageous to choose Circular entropy then Cauchy entropy (p < 0.001) over the standard techniques, in order to discriminate fetal heart rates.