Abstract
We introduce a new flexible modified alpha power (MAP) family of distributions by adding two parameters to a baseline model. Some of its mathematical properties are addressed. We show empirically that the new family is a good competitor to the Beta-F and Kumaraswamy-F classes, which have been widely applied in several areas. A new extension of the exponential distribution, called the modified alpha power exponential (MAPE) distribution, is defined by applying the MAP transformation to the exponential distribution. Some properties and maximum likelihood estimates are provided for this distribution. We analyze three real datasets to compare the flexibility of the MAPE distribution to the exponential, Weibull, Marshall-Olkin exponential and alpha power exponential distributions.