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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.
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