A stochastic diffusion model of Lorenz Curve with a birth-and-death diffusion and general external effect processes

The Lorenz curve has been used as an essential instrument in the studies of inequality of wealth and income distributions. It was further devised as an inequality research tool in many disciplines. A stochastic Lorenz Curve model is considered with a birth-and-death diffusion and general external effect processes in this paper. Also, the corresponding Stochastic Diffusion Gini-Index is obtained. The suggested functional form attains the properties of the Lorenz curve and works nicely, as shown in the numerical example.