Statistical characterization of two-level random telegraph noise (RTN) amplitude distribution in a hafnium oxide resistive memory has been performed. We find that two-level RTN in HRS exhibits a large amplitude distribution tail, as compared to LRS. To investigate an RTN trap position in a hafnium oxide film, we measure the dependence of electron capture and emission times of RTN on applied read voltage. A correlation between an RTN trap position and RTN amplitude is found. A quasi-two-dimensional RTN amplitude simulation based on trap-assisted electron sequential tunneling is developed. Our study shows that RTN traps in a rupture region of a hafnium oxide film are responsible for an RTN large-amplitude tail in HRS mostly.