Compound Exponential Power Distribution and its Application to Microarray Data

The compound distributions have applications in many fields including insurance. The present paper introduces a new family of Exponential power distribution called compound Exponential power distribution, which is obtained by compounding the exponential power distribution with the gamma distribution. This family of distribution includes the Laplace and normal distributions as special cases. We discuss various properties of this distribution. The maximum likelihood estimation procedure is employed to estimate the parameters of the proposed distribution and an algorithm in R package is developed to carry out the estimation. Simulation studies for various choices of parameter values are performed to validate the algorithm. Finally, we illustrate the application using microarray gene expression data.