The generalized odd half-Cauchy family of distributions: Properties and applications

We introduce and study general mathematical properties of a new generator of continuous distributions with one extra parameter called the generalized odd half-Cauchy family. We present some special models and investigate the asymptotics and shapes. The new density function can be expressed as a linear mixture of exponentiated densities based on the same baseline distribution. We derive a power series for the quantile function. We discuss the estimation of the model parameters by maximum likelihood and prove empirically the flexibility of the new family by means of two real data sets.