Fast Radio Bursts (FRBs) are extremely energetic (1029 -1032 J) short (millisecond) pulses of radio waves of cosmological origin that their progenitors and emission mechanism remain unsolved, although discovered more than a decade and a half ago. Extragalactic highly magnetized neutron stars (magnetars) are among the candidate progenitors of FRBs. The recent emission of an FRB and FRB-like bursts accompanied by X-Ray bursts from the galactic magnetar SGR 1935+2154 strengthened this proposition and called for a detailed scrutiny of the proposed association. Through this thesis we tackle this by studying a set of recurrent FRBs (that show a repeating behavior from the same location) together with similarly energetic X-ray bursts (intermediate flares) of confirmed magnetar origin. We utilized the first catalog of the Canadian Hydrogen Intensity Mapping Experiment (CHIME) radio observatory’s and identified 62 repeating extragalactic FRB in the 400-800 MHz frequency range, and 54 X-ray intermediate flares from five galactic magnetars. The duration (T), flux (F) and fluence (S) of the repeating FRBs showed lognormal distributions with means of 8.76 ± 1.00 ms, (3.15 ± 0.37) ×10−15 erg s−1 cm−2 and (2.76 ± 0.07) ×10−17 erg s−1 , respectively. Empirical relations between those quantities were found to follow the power-law relations: SF RB ∝ T 0.49 F RB and FF RB ∝ T −0.52 F RB . The X-ray intermediate flares showed similar lognormal trends for the same properties with their means given by 0.94 ± 0.06 s, (9.69 ± 0.69) × 10−6 erg s−1 cm−2 and (9.96 ± 0.65) × 10−6 erg cm−2 . The corresponding empirical correlations were found to be SIF ∝ T 0.67 IF and FIF ∝ T −0.32 IF . Our results favor the pulsar-like emission models that involve compact objects, such as neutron stars, over the cataclysmic event models that involve exploding stars or the merger of compact objects