α-Power transformed transformed power function distribution with applications.

By standard transformation of a random variable, we obtained a partially bounded one-parameter version of the bounded three-parameter power function distribution by Saran and Pandey (2004) which we called the Transformed Power Function (TPF) distribution and based on an alpha-power transformation method due to Mahdavi and Kundu (2017) we generalized the TPF distribution as the α-Power Transformed Transformed Power Function (αPTTPF) distribution. Some of the properties of the αPTTPF distribution are given, and we approached the parameter estimation by three methods, namely: maximum likelihood, ordinary least-squares, and weighted least-squares, but after comparing the results from a simulation study, we settled for the maximum likelihood. The new distribution is suitable for modeling data with either decreasing or upside-down bathtub hazard rates. Three real data-sets are used to demonstrate the usefulness of the new model.