  The framework of differential privacy protects an individual's privacy while
publishing query responses on congregated data. In this work, a new noise
addition mechanism for differential privacy is introduced where the noise added
is sampled from a hybrid density that resembles Laplace in the centre and
Gaussian in the tail. With a sharper centre and light, sub-Gaussian tail, this
density has the best characteristics of both distributions. We theoretically
analyze the proposed mechanism, and we derive the necessary and sufficient
condition in one dimension and a sufficient condition in high dimensions for
the mechanism to guarantee (${\epsilon}$,${\delta}$)-differential privacy.
Numerical simulations corroborate the efficacy of the proposed mechanism
compared to other existing mechanisms in achieving a better trade-off between
privacy and accuracy.
