Abstract: The use of tail risk measures has been noticed in recent decades, especially in the financial and banking industry. The most common ones are value at risk and expected shortfall. The tail Gini risk measure, a composite risk measure, was introduced recently. The primary purpose of this article is to find the relationship between the concepts of economic risks, especially the expected shortfall and the tail Gini risk measure, with the concepts of inequality indices in the economy and reliability. Examining the relationship between these concepts allows the researcher to use the concepts of one to investigate other concepts. As you will see below, the existing mathematical relationships between the tail risk measures and the mentioned indices have been obtained, and these relationships have been calculated for some distributions. Finally, real data from the Iranian Stock Exchange was used to familiarize the concept of this tail risk measure.