Sushila-Geometric distribution, properties, and applications

In the present paper, we introduce a compound form of the Sushila distribution which offers a flexible modelfor lifetime data, the so-called Sushila-geometric $(SG)$ distribution, and is obtained by compounding Sushila and geometric distributions. A three-parameter $SG$ distribution is capable of modelling upside-down bathtub, bathtub-shaped, increasing and decreasing hazard rate functions which are widely used in engineering, economy and natural sciences. This new model contains some known distributions such as Lindley, Lindley-Geometric, and Sushila distributions in a special cases as sub-models. Several statistical properties of the $SG$ distribution are derived. Simulation studies are conducted to investigate the performance of the maximum likelihood estimators derived through the EM algorithm. The flexibility of the new model is illustrated in the application of two real data sets.