A new five-parameter model called the modified beta Weibull probability distribution is being introduced in this paper. This model turns out to be quite flexible for analyzing positive data and has bathtub and upside down bathtub hazard rate function. Our main objectives are to obtain representations of certain statistical functions and to estimate the parameters of the proposed distribution. As an application, the probability density function is utilized to model two actual data sets. The new distribution is shown to provide a better fit than related distributions. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling positive data arising in various fields of scientific investigation such as reliability theory, hydrology, medicine, meteorology, survival analysis and engineering.