Abstract.: A three-parameter probability distribution is derived from a composed cumulative distribution function, which is itself a family of bounded support transformations. The transformed model called the doubly bounded exponential distribution, which exhibits decreasing shaped density while the hazard rate has increasing shape. Some statistical properties are obtained in closed form, such as the moments and various entropy functions. The parameter estimation is carried out by the methods of maximum likelihood estimate, least squares estimate, weighted least squares estimate, Anderson-Darling estimate, and Cramér-von Mises estimate. The performance of these estimators is assessed through a Monte Carlo simulation study. The identifiability of the DB-Exp model’s parameters is also investigated. The proposed distribution can produce a higher performance than several well-known bounded distributions in the literature, as shown by an application to rainfall data.