|
Lorenz Curve
In economics, the Lorenz curve is a graphical representation of the distribution of income or of wealth. It was developed by Max O. Lorenz in 1905 for representing inequality of the wealth distribution. The curve is a graph showing the proportion of overall income or wealth assumed by the bottom ''x''% of the people, although this is not rigorously true for a finite population (see below). It is often used to represent income distribution, where it shows for the bottom ''x''% of households, what percentage (''y''%) of the total income they have. The percentage of households is plotted on the ''x''-axis, the percentage of income on the ''y''-axis. It can also be used to show distribution of assets. In such use, many economists consider it to be a measure of social inequality. The concept is useful in describing inequality among the size of individuals in ecology and in studies of biodiversity, where the cumulative proportion of species is plotted against the cumulative pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Economics Gini Coefficient2
Economics () is the social science that studies the production, distribution, and consumption of goods and services. Economics focuses on the behaviour and interactions of economic agents and how economies work. Microeconomics analyzes what's viewed as basic elements in the economy, including individual agents and markets, their interactions, and the outcomes of interactions. Individual agents may include, for example, households, firms, buyers, and sellers. Macroeconomics analyzes the economy as a system where production, consumption, saving, and investment interact, and factors affecting it: employment of the resources of labour, capital, and land, currency inflation, economic growth, and public policies that have impact on these elements. Other broad distinctions within economics include those between positive economics, describing "what is", and normative economics, advocating "what ought to be"; between economic theory and applied economics; between rational and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Debt
Debt is an obligation that requires one party, the debtor, to pay money or other agreed-upon value to another party, the creditor. Debt is a deferred payment, or series of payments, which differentiates it from an immediate purchase. The debt may be owed by sovereign state or country, local government, company, or an individual. Commercial debt is generally subject to contractual terms regarding the amount and timing of repayments of principal and interest. Loans, bonds, notes, and mortgages are all types of debt. In financial accounting, debt is a type of financial transaction, as distinct from equity. The term can also be used metaphorically to cover moral obligations and other interactions not based on a monetary value. For example, in Western cultures, a person who has been helped by a second person is sometimes said to owe a "debt of gratitude" to the second person. Etymology The English term "debt" was first used in the late 13th century. The term "debt" com ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lorenz Curve Of Denmark, Hungary, And Namibia
Lorenz is an originally German name derived from the Roman surname Laurentius, which means "from Laurentum". Given name People with the given name Lorenz include: * Prince Lorenz of Belgium (born 1955), member of the Belgian royal family by his marriage with Princess Astrid of Belgium * Lorenz Böhler (1885–1973), Austrian trauma surgeon * Lorenz Hart (1895–1943), American lyricist, half of the famed Broadway songwriting team Rodgers and Hart * Lorenz Lange (1690–1752), Russian official in Siberia * Lorenz Oken (1779–1851), German naturalist * Lorenz of Werle (1338/40–1393/94), Lord of Werle-Güstrow Surname People with the name surname Lorenz include: * Adolf Lorenz (1854–1946), Austrian surgeon * Alfred Lorenz (1868–1939), Austrian-German musical analyst * Angela Lorenz (born 1965), American artist * Barbara Lorenz, make-up artist * Carl Lorenz (1913–1993), German cyclist * Christian Lorenz (born 1966), German musician * Edward Norton Lorenz (1917– ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pareto Distribution
The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto ( ), is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population. The Pareto principle or "80-20 rule" stating that 80% of outcomes are due to 20% of causes was named in honour of Pareto, but the concepts are distinct, and only Pareto distributions with shape value () of log45 ≈ 1.16 precisely reflect it. Empirical observation has shown that this 80-20 distribution fits a wide range of cases, including natural phenomena and human activities. Definitions If ''X'' is a random variable with a Pareto (Type I) distribution, then the probability that ''X'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infimum
In mathematics, the infimum (abbreviated inf; plural infima) of a subset S of a partially ordered set P is a greatest element in P that is less than or equal to each element of S, if such an element exists. Consequently, the term ''greatest lower bound'' (abbreviated as ) is also commonly used. The supremum (abbreviated sup; plural suprema) of a subset S of a partially ordered set P is the least element in P that is greater than or equal to each element of S, if such an element exists. Consequently, the supremum is also referred to as the ''least upper bound'' (or ). The infimum is in a precise sense dual to the concept of a supremum. Infima and suprema of real numbers are common special cases that are important in analysis, and especially in Lebesgue integration. However, the general definitions remain valid in the more abstract setting of order theory where arbitrary partially ordered sets are considered. The concepts of infimum and supremum are close to minimum and max ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cumulative Distribution Function
In probability theory and statistics, the cumulative distribution function (CDF) of a real-valued random variable X, or just distribution function of X, evaluated at x, is the probability that X will take a value less than or equal to x. Every probability distribution supported on the real numbers, discrete or "mixed" as well as continuous, is uniquely identified by an ''upwards continuous'' ''monotonic increasing'' cumulative distribution function F : \mathbb R \rightarrow ,1/math> satisfying \lim_F(x)=0 and \lim_F(x)=1. In the case of a scalar continuous distribution, it gives the area under the probability density function from minus infinity to x. Cumulative distribution functions are also used to specify the distribution of multivariate random variables. Definition The cumulative distribution function of a real-valued random variable X is the function given by where the right-hand side represents the probability that the random variable X takes on a value less th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Density Function
In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can be interpreted as providing a ''relative likelihood'' that the value of the random variable would be close to that sample. Probability density is the probability per unit length, in other words, while the ''absolute likelihood'' for a continuous random variable to take on any particular value is 0 (since there is an infinite set of possible values to begin with), the value of the PDF at two different samples can be used to infer, in any particular draw of the random variable, how much more likely it is that the random variable would be close to one sample compared to the other sample. In a more precise sense, the PDF is used to specify the probability of the random variable falling ''within a particular range of values'', as opposed ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Distribution
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of would take the value 0.5 (1 in 2 or 1/2) for , and 0.5 for (assuming that the coin is fair). Examples of random phenomena include the weather conditions at some future date, the height of a randomly selected person, the fraction of male students in a school, the results of a survey to be conducted, etc. Introduction A probability distribution is a mathematical description of the probabilities of events, subsets of the sample space. The sample space, often denoted by \Omega, is the set of all possible outcomes of a random phe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Continuous Function
In mathematics, a continuous function is a function such that a continuous variation (that is a change without jump) of the argument induces a continuous variation of the value of the function. This means that there are no abrupt changes in value, known as '' discontinuities''. More precisely, a function is continuous if arbitrarily small changes in its value can be assured by restricting to sufficiently small changes of its argument. A discontinuous function is a function that is . Up until the 19th century, mathematicians largely relied on intuitive notions of continuity, and considered only continuous functions. The epsilon–delta definition of a limit was introduced to formalize the definition of continuity. Continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. The concept has been generalized to functions between metric spaces and between topological spaces. The latter are t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a mathematical formalization of a quantity or object which depends on random events. It is a mapping or a function from possible outcomes (e.g., the possible upper sides of a flipped coin such as heads H and tails T) in a sample space (e.g., the set \) to a measurable space, often the real numbers (e.g., \ in which 1 corresponding to H and -1 corresponding to T). Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice; it may also represent uncertainty, such as measurement error. However, the interpretation of probability is philosophically complicated, and even in specific cases is not always straightforward. The purely mathematical analysis of random variables is independent of such interpretational difficulties, and can be based upon a rigorous axiomatic setup. In the formal mathematical language of measure theory, a random ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
P–P Plot
In statistics, a P–P plot (probability–probability plot or percent–percent plot or P value plot) is a probability plot for assessing how closely two data sets agree, or for assessing how closely a dataset fits a particular model. It works by plotting the two cumulative distribution functions against each other; if they are similar, the data will appear to be nearly a straight line. This behavior is similar to that of the more widely used Q–Q plot, with which it is often confused. Definition A P–P plot plots two cumulative distribution functions (cdfs) against each other: given two probability distributions, with cdfs "''F''" and "''G''", it plots (F(z),G(z)) as ''z'' ranges from -\infty to \infty. As a cdf has range ,1 the domain of this parametric graph is (-\infty,\infty) and the range is the unit square ,1times ,1 Thus for input ''z'' the output is the pair of numbers giving what ''percentage'' of ''f'' and what ''percentage'' of ''g'' fall at or below ''z.'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
.svg "Click for more on -> Continuous Distribution")
