SEMCIÊNCIA

The formula is T = 1/N \sum (x_i/[x] ) ln (x_i/[x] ) where x_i is the income of the ith person, [x] is the mean income (não consigo colocar overbar ou brackets aqui), and N is the number of people. The first term inside the sum can be considered the individual's share of aggregate income, and the second term is that person's income relative to the mean. If everyone has the same (i.e., mean) income, then the index = 0. If one person has all the income, then the index = lnN. The Theil index is derived from Shannon 's measure of information entropy . Letting T be the Theil Index and S be Shannon's information entropy measure,T = ln(N) − S. Shannon derived his entropy measure in terms of the probability of an event occurring. This can be interpreted in the Theil index as the probability a dollar drawn at random from the population came from a specific individual. This is the same as the first term, the individual's share of aggregate income. Theil's index takes an ...