in general depend on both N and the inequality of firms' shares. The "number of effective competitors" is the inverse of the Herfindahl index. Terrence Kavyu Muthoka defines distribution just as functionals in the Swartz space which is the space of functions with compact support and with all derivatives existing. The or the Dirac function is a good example. (b) The Linda index (1976) where Qi is the ratio between the average share of the first firms and the average share of the remaining firms and is the concentration coefficient for the first firms. Although it doesn't capture the peripheral firms like the HHI formula, it works to capture the "core" of the market, and masure the degree of inequality between the size variable accounted for by various sib-samples of firms. This index, does assume pre-calculation on the users' behalf to determine the relevant value of However, there is little empirical evidence of regulatory usage of the Linda Index. (c) Comprehensive concentration index (Horwath 1970): Where s1 is the share of the largest firm. The index is similar to except that greater weight is assigned to the share of the largest firm. When compared to the HHI index, it does present some advantages, such as giving more weight to the quantity of small firms, however the arbitrary choice to only include the absolute value of one firm has led to criticism over its accuracy and usefulness. (d) The Rosenbluth (1961) index (also Hall and Tideman, 1967): where symbol i indicates the firm's rank position. The Rosenbluth index assigns more weight to smaller competitors when there are more firms present in the marketplace, and is sensitive to the amount of competitors in the market, even if there is a small amount of large firms dominating. Its coefficients and ranking are similar to results produced through the use of the Herfindahl-Hirschman Index. (e) The Gini coefficient (1912) The Gini coefficient measures the difference between firms' sizes without including the number of firms operating in a market. This is known as a relative concentration measure and differs from absolute concentration measures (like the Rosenbluth index) which includes the number of firms and firms' distribution sizes. It is used in conjunction with the Lorenz curve. Originally, the Lorenz curve measured the inequality of income distributed with a population and ranked individuals from highest to lowest earnings. Therefore, in this context the Gini coefficient is