Abstract
Existence of many models for the distribution of income leads to difficulty of selection to the best model for the distribution of income, So the importance of this paper is through knowledge of best probability distribution for the average member income in Iraq and measure the level of social and economic welfare of the member through Peugeot index for two years (2007, 2012) at city and countryside regions where the use of statistical software (Release(R)) (ver. 3.0.1) and statistical program (matlab) and excel software to analyze and extract the results.The statistical program (R) was used to estimate the parameters and founding χ^2 values and computes Gini value for income distributions in (2007, 2012) according to city and countryside region. and the statistical program (matlab) is used to estimate the parameters and founding χ^2 for generalized beta distribution with five parameters .By the result, we are reaching from (R) in 2007 to all the governorates in Iraq and according to countryside and city regions that beta (tybe1) distribution in many governorates is the best probability distribution. When the value of Gini coefficient is (zero and sometimes very close to (zero), lama the level of social and economic welfare was a little low especially at the countryside regions. As well as in 2012 where it's shown that beta (tybe1) distribution is the best probability distribution in many governorates at according countryside and city economic welfare was a little low because of the increasing of inequality in the income distribution between members.The statistical program excel is used to represent the evolution of the income structure by graphical.We are reaching that inequality in the income distribution in 2007 simple or un noticeable and in 2012 is the biggest or noticeable between the averages of member in income.
