The Total time on test transform in measuring income inequality

Wealth distribution is one of the most important and effective factors in the economic and social stability of each society. Thus, assessing the behavior of income distribution have great importance and to do this, several indices have been introduced that their performance has been investigated in terms of precision. The main goal of this paper is to introduce the Total Time on Test (TTT) transformation and its corresponding graph as a beneficial index for measuring income inequality. We further compare its performance with the Lorentz and Zanga indices. The micro-data of Iranian household income in the period 2012-2018 has been used to analyze the performance of the proposed index. The results show that while the new index performs better than the Lorenz one, it performs as same as the Zenga index. We also introduced a new distorted model using distortion functions in the final section, and by considering the basement income distribution, the generalized version of these distributions are presented and some of their features, particularly the maximum likelihood estimator are investigated. In addition, the goodness of fit of the new distributions to the income data of citizens in Texas (Arnold 1983) and the income data of Iranian households in 2017 are other results of this article.