New multi-parametric analytical approximations of exponential distribution with power law tails for new cars sells and other applications

Abstract

A multi-parametric family of exponential distributions with various power law tails is introduced and is shown to describe adequately the known distributions of incomes and wealth as well as the recently measured distributions of new car sales. The three or four-parametric families are characterized by effective temperature in the exponential part, the power exponent in the power-law asymptotic part, the coefficient for the transition between the above two parts, and the starting value, if it is not equal to zero. Since the new car sales distributions are found to correspond to known distributions of incomes, the latter may be inferred from the former.