Abstract. Lorenz curve is an important tool to measure income inequality. Many indices are defined based on Lorenz curve to measure the inequality; Gini coefficient is one of them.

In this paper, we introduce Lorenz curve and Gini coefficient and we estimate the unknown parameters of income probability distribution by the maximum likelihood method. Functional forms of the Lorenz curve are estimated via two methods and the best functional form is introduced.

Finally, we estimate the Lorenz curve and the Gini coefficient based on the data of household income and expenditure survey of Iran 2005.