A Method to Expand Family of Continuous Distributions based on Truncated Distributions

A new method to generate various family of distributions is introduced. This method introduces a new two-parameter extension of the exponential distribution to illustrate its application. Some statistical and reliability properties of the new distribution, including explicit expressions for the moments, quantiles, mode, moment generating function, mean residual lifetime, stochastic orders, order statistics and some entropies are discussed. Maximum likelihood method is used to estimate the unknown parameters and the Fisher information matrix is given. The obtained results are validated using a real data set and it is shown that the new family provides a better fit than some other known distributions.