Probability distributions and their families play an effective role in statistical modeling and statistical analysis. Recently, researchers have been increasingly interested in generating new families with high flexibility and low number of milestones. We propose and study a new family of continuous distributions. Relevant properties are presented. Many bivariate versions of the new family are derived under the Farlie-Gumbel-Morgenstern copula, modified Farlie-Gumbel-Morgenstern copula, Clayton

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... copula, entropy copula and Ali-Mikhail-Haq copula. We present two characterizations of the new family. Different estimation methods such as the maximum likelihood estimation, maximum product spacing estimation, least squares estimation, weighted least squares estimation, Anderson-Darling estimation and the Cramer-von Mises estimation methods are considered. Simulation studies for comparing estimation methods are performed based on the baseline Lindley model. Two real data sets are analyzed for comparing the competitive models.