The power-law distribution for the income of poor households

This study proposes a reverse Pareto model to describe the power-law behavior for the lower tail data of income distribution and illustrates an application on Malaysian and Italian household income data. A robust method based on probability integral transform statistic is used for estimating the shape parameter of the reverse Pareto model to allow for the existence of outlying observations in the lower tail data. Besides that, the optimal threshold of reverse Pareto is determined by using Kolmogorov–Smirnov statistic. It is found that the fitted reverse Pareto adequately describes the lower tail data of both datasets, suggesting that the power-law behavior is obeyed. In addition, the estimated optimal threshold of reverse Pareto model can be utilized as an alternative measure for the relative poverty line. Based on the reverse Pareto model, the Lorenz curve, Gini and Theil coefficients are determined, and it is found that low income inequality is observed for the period of the study. The fitted Lorenz curve shows that nearly 80% of the total household income is owned by the bottom 80%, whereas the remaining total household income is owned by the top 20%. Finally, comparison of the reverse Pareto model with some alternative distributions such as shifted reverse exponential, shifted reverse stretched exponential and shifted reverse lognormal in terms of model fitting for the lower tail data is also conducted. The results show that the reverse Pareto model outperform all the other models.