Parametric Lorenz Curves and its Relationship with Reliability Indicators

The problem of poverty can not be considered without paying care to the topic of income distribution. In fact, the concept of poverty refers to the lowest class in the distribution of income, and inequality in the income distribution is related to all stages of society. Based on the income distributions that are unfairly priced, many indices have been developed to measure the size of inequality in the economy (wroth income distribution). The Lorenz curve is an important tool for measuring the income inequality. One method of estimating the Lorenz curve is to use a parametric form of Lorenz curve on the data. In this paper, we introduce some parameters of Lorenz curves and introduced the popular parametric models to the Iranian income and expenditure data to year 1395 and choose the best model. Finally, we calculate the quantile function corresponding to the introduced models.