A new continuous distribution is introduced by compounding exponentiated exponential and binomial distributions, named as exponentiated exponential binomial (EEB) distribution. This distribution has the ability to model lifetime data with increasing, decreasing and upside-down bathtub shaped failure rates. Moreover, the zero-truncated binomial distribution used in compounding is overdispersed. Some properties of the distribution are investigated. Estimation and inference procedure for the distribution parameters are discussed. An application to real data demonstrates that the EEB distribution can provide a better fit than a recent class of lifetime distributions
