We introduce a new skew version of the well-known symmetric Cauchy probability distribution using quantile function approach. This approach is based on splitting the quantile function of the Cauchy distribution into two other quantile functions of some distributions. The original definition of the new distribution has an extra skewness parameter besides location and scale parameters. We also introduce an additional shape parameter to the distribution in order to enhance the flexibility of the distribution in data fitting. The proposed distribution is mathematically more tractable than the other forms defined in the literature and basic properties of the distribution are derived. Several parameter estimation methods are proposed. The results of a simulation study to compare the performances of the estimators are reported. Two real data fitting applications are also given. The results show that the newly defined distribution can be a useful alternative in modeling skew non-normal data.
Alі İ. Genç (Sun,) studied this question.