A bottom poor sensitive Gini coefficient and maximum entropy estimation of income distributions

A bottom poor sensitive Gini coefficient (pgini) is defined by replacing income observations with their reciprocal values in the Gini coefficient. The underlying true income share function can be derived approximately using the maximum entropy method given the pgini coefficient.

► Poverty sensitive Gini coefficient is derived using the reciprocal income shares. ► Reciprocal income value defines the inconvenience level of each person. ► Inconvenience inequality measures relative pains of various inconvenience groups. ► Income share function is approximated from the Gini using Maximum entropy method. ► Inconvenience inequality measure can be extended for Theil index and Atkinson index.