For at least a century academics and governmental researchers have been developing measures that would aid them in understanding income distributions, their differences with respect to geographic regions, and changes over time periods. It is a fascinating area due to a number of reasons, one of them being the fact that different measures, or indices, are needed to reveal different features of income distributions. The existing indices, the Gini index, the Bonferroni index and the Zenga index are intrinsically linked each other, whereas their emphasis are laid differently. One of the limitations of the existing indices is that they provide an overall measurement for the whole society and cannot distinguish the distributions with the same index value. This thesis works on the extension of the three indices and proposes a new index which can make comparison between any groups with different income level, for example, the richest group and the poorest group. The new index satisfies the axioms of inequality measures. The statistical inferential results of the new index are derived and their performance are tested by a simulation study and the results are used to analyze the income data of Hong Kong from Census and Statistics Department, HKSAR. / 近一個世紀學術界和政府間的研究人員一直致力於創造和發展可以幫助理解不同國家地區收入分布和差異的測度。很多原因使之成為令人感興趣的研究領域，需要不同測度或指數用以理解收入分布的不同特征便是原因之一。Gini指數，Bonferroni 指數和Zenga指數等現有指數在本質上相互聯系，但側重點各有不同。可以對整個社會有一個整體測度而不能對具有相同指數的收入分布進行區分是現有指數的共同缺陷。本論文基於以上三種指數提出一種新的指數可以在不同收入水平間進行比較，例如，最富有階層和最貧困階層。新指數滿足收入不均測度的相關性質。本論文推導出新指數的相關統計推理結果並用數值模擬實驗進行了測試，最終用其結果對香港政府統計處的人口普查數據進行了分析。 / Chen, Teng. / Thesis M.Phil. Chinese University of Hong Kong 2015. / Includes bibliographical references (leaves 59-61). / Abstracts also in Chinese. / Title from PDF title page (viewed on 05, October, 2016). / Detailed summary in vernacular field only.