Abstract
We introduce and study the beta exponentiated Nadarajah-Haghighi model, which has increasing, decreasing, upside-down bathtub and bathtub shaped hazard functions. Some of its mathematical properties are determined including a power series for the quantile function. We perform a Monte Carlo simulation study to assess the finite sample behavior of the maximum likelihood estimates of the parameters. We define a new regression model based on the new distribution. The potentiality of this regression model is proved empirically by means of a real dataset related to diabetic retinopathy study.