A new formulation of generalized gamma: Some results and applications

We extend the 2-parameter Weibull to the generalized gamma distribution by adding a new partial parameter. The new shape parameter can be used to easily generate generalized gamma distributions with different shapes of the density function, hazard rate, and mean residual lifetimes that are useful in simulating various business processes such as manufacturing processes, and reliability systems. We derived some theoretical results and created visual presentations to demonstrate the behaviors of this new shape parameter as well. A new Monte Carlo simulation based on the new parameter was proposed to assess the discrepancy between the generalized gamma and its subfamilies. The power analysis of the proposed test was evaluated via simulation studies. We also present some numerical examples.