In this paper, a flexible model called extended Chen (EC) distribution is derived from the generalized Burr-Hatke differential equation and nexus between the exponential and gamma variables. The EC distribution is also derived from compounding mixture of the generalized Chen and gamma distributions. The EC distribution is very flexible and its hazard rate function accommodates various shapes such as increasing, decreasing, decreasing–increasing, increasing–decreasing–increasing, bathtub and modified bathtub. The density function of the EC model is arc, J, reverse-J, left-skewed, right-skewed and symmetrical shaped. Some structural and mathematical properties such as descriptive measures on the basis of quantiles, stochastic orderings, moments, order statistics and reliability measures are theoretically established. The EC distribution is characterized via various techniques. The maximum likelihood estimates for unknown parameters of the EC distribution are obtained. A simulation study is executed to assess the behavior of the maximum likelihood estimators. The EC distribution is applied to two real data sets to elucidate its potentiality and utility. The competence of the EC distribution is tested through various goodness of fit criteria.