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If Kraft's inequality holds with strict inequality, the code has some redundancy. If Kraft's inequality holds with equality, the code in question is a complete code. [2] If Kraft's inequality does not hold, the code is not uniquely decodable. For every uniquely decodable code, there exists a prefix code with the same length distribution.
In mathematics, the following inequality is known as Titu's lemma, Bergström's inequality, Engel's form or Sedrakyan's inequality, respectively, referring to the article About the applications of one useful inequality of Nairi Sedrakyan published in 1997, [1] to the book Problem-solving strategies of Arthur Engel published in 1998 and to the book Mathematical Olympiad Treasures of Titu ...
Because it is not possible to score DIT-1 and DIT-2 personally, the Center of Ethical Development at the University of Alabama offers scoring to scholars and researchers worldwide. [ 3 ] The Defining Issues Test is a proprietary self-report measure [ 4 ] which uses a Likert-type scale to give quantitative ratings and rankings to issues ...
Bennett's inequality, an upper bound on the probability that the sum of independent random variables deviates from its expected value by more than any specified amount Bhatia–Davis inequality , an upper bound on the variance of any bounded probability distribution
Proof [2]. Since + =, =. A graph = on the -plane is thus also a graph =. From sketching a visual representation of the integrals of the area between this curve and the axes, and the area in the rectangle bounded by the lines =, =, =, =, and the fact that is always increasing for increasing and vice versa, we can see that upper bounds the area of the rectangle below the curve (with equality ...
Bernoulli's inequality can be proved for case 2, in which is a non-negative integer and , using mathematical induction in the following form: we prove the inequality for r ∈ { 0 , 1 } {\displaystyle r\in \{0,1\}} ,
The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and is the mean income.. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean).
In economics, the Gini coefficient (/ ˈ dʒ iː n i / JEE-nee), also known as the Gini index or Gini ratio, is a measure of statistical dispersion intended to represent the income inequality, the wealth inequality, or the consumption inequality [2] within a nation or a social group.