“…For market-economy countries, it has been empirically observed that the income structure of top income class (less than 5% of populations) obeys a Pareto distribution (Mandelbrot, 1960;Nirei and Souma, 2007;Atkinson et al, 2011;Aoki and Nirei, 2017;Tao et al, 2019), while the low-and middle-income class (about 95% of populations) obeys an exponential distribution (Nirei and Souma, 2007;Newby et al, 2011;Clementi et al, 2012;Prinz, 2016;Irwin and Irwin, 2017;Rosser, 2019;Tao et al, 2019;Ma and Ruzic, 2020). Theoretically, it has been known that the generalized Pareto distribution is a fairly general family that includes the Pareto distribution and the exponential distribution as two special cases (Balkema and Haan, 1974;Pickands, 1975;Singh and Maddala, 1976;Cowell, 2000).…”