In statistics, it is always desired to generate new distributions in order to get more flexible real lifetime data fitting. The literature is rich of studies that aim to introducing new probability models and still growing rapidly. A few expansions of some outstanding lifetime disseminations have been created since last two decades for demonstrating and examinations numerous kinds of genuine information that having diverse arbitrary nature. In the present paper, a new family of transmuted distribution function, the cubic transmuted power function distribution (CTPFD), is introduced. Explicit formulae for its probability density function and cumulative distribution function are written. The statistical properties and some descriptive measures are studied. The moment matching estimation and maximum likelihood estimation for estimating the unknown distribution parameters are used. The properties of the estimators (biases, mean squared errors, and confidence intervals) are investigated via Monte Carlo simulation analysis. Three data sets have been considered for investigating the usefulness of CTPFD and have observed that our proposed distribution performs better than other probability models used in the analysis.