On the Log-Concavity Density Function: A Case of Exponential Power Distribution and its Application

Abstract

Log-concavity of probability density functions has played an important role in many applications in economics, reliability studies, and many more. Several authors have studied log-concavity of many distribution such as the normal, logistic, exponential, etc., but no attention has been paid to exponential power distributions, a family of elliptical distributions which generalize the normal, double exponential, and Kotz distribution. This distribution has been found to be very useful in applications, especially when flexibility of the tails (heavier or thinner than the normal distribution) are required in modeling of natural phenomenon. This paper was written to fill this void in the literature.