| In this work we study a class of univariate asymmetric distributions. This flexible four parameter family of skew exponential power (EP) laws includes (symmetric as well as skew) Laplace and normal distributions. We discuss basic properties of skew EP laws and derive their moments and related parameters, including skewness, kurtosis, and entropy. Extending the symmetric EP and the skew Laplace cases, we obtain a representation of a skew EP variable that is useful in random variate generation from this distribution. We establish maximum entropy characterization of symmetric and skew EP laws, and derive the maximum likelihood estimators for the skew EP parameters. We conclude with a discussion of possible applications of skew EP laws in mathematical finance. Our practical example of fitting EP laws to currency exchange rate data indicates that skew EP laws might be useful in this area. |
