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We obtain some mathematical properties of a new generator of continuous distributions with two additional shape parameters called the odd log-logistic geometric family. We present some special models and investigate the asymptotes and shapes. The family density function can be expressed as a linear combination of exponentiated densities based on the same baseline distribution. We derive a power series for its quantile function. We provide explicit expressions for the ordinary and incomplete moments and generating function. We estimate the model parameters by maximum likelihood. We propose a useful regression model by varying the dispersion parameter to fit real data. We illustrate the potentiality of the proposed models by means of three real data sets.

The Odd Log-Logistic Geometric Family with Applications in Regression Models with Varying Dispersion