An econophysical approach of polynomial distribution applied to income and expenditure

Abstract: Polynomial distribution can be applied to dynamical systems in certain situations. Macroeconomic systems characterized by economic variables such as income and wealth can be modelled similarly using polynomials. We extend our previous work to data regarding income from a more diversified pool of countries, which contains developed countries with high income, developed countries with middle income, developing and underdeveloped countries. Also, for the first time we look at the applicability of polynomial distribution to expenditure (consumption). Using cumulative distribution function, we found that polynomials are applicable with a high degree of success to the distribution of income to all countries considered without significant differences. Moreover, expenditure data can be fitted very well by this polynomial distribution. We considered a distribution to be robust if the values for coefficient of determination are higher than 90%. Using this criterion, we decided the degree for the polynomials used in our analysis by trying to minimize the number of coefficients, respectively first or second degree. Lastly, we look at possible correlation between the values from coefficient of determination and Gini coefficient for disposable income.