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Mean Log Deviation
In statistics and econometrics, the mean log deviation (MLD) is a measure of income inequality. The MLD is zero when everyone has the same income, and takes larger positive values as incomes become more unequal, especially at the high end. Definition The MLD of household income has been defined asJonathan Haughton and Shahidur R. Khandker. 2009. ''The Handbook on Poverty and Inequality''. Washington, DC: The World Bank. : \mathrm=\frac\sum_^N \ln \frac where N is the number of households, x_i is the income of household ''i'', and \overline is the mean of x_i. Naturally the same formula can be used for positive variables other than income and for units of observation other than households. Equivalent definitions are : \mathrm=\frac\sum_^N (\ln \overline - \ln x_i) =\ln \overline - \overline where \overline is the mean of ln(''x''). The last definition shows that MLD is nonnegative, since \ln \geq \overline by Jensen's inequality. MLD has been called "the standard dev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. Representative sampling assures that inferences and conclusions can reasonably extend from the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Econometrics
Econometrics is the application of statistical methods to economic data in order to give empirical content to economic relationships. M. Hashem Pesaran (1987). "Econometrics," '' The New Palgrave: A Dictionary of Economics'', v. 2, p. 8 p. 8–22 Reprinted in J. Eatwell ''et al.'', eds. (1990). ''Econometrics: The New Palgrave''p. 1 p. 1–34Abstract ( 2008 revision by J. Geweke, J. Horowitz, and H. P. Pesaran). More precisely, it is "the quantitative analysis of actual economic phenomena based on the concurrent development of theory and observation, related by appropriate methods of inference". An introductory economics textbook describes econometrics as allowing economists "to sift through mountains of data to extract simple relationships". Jan Tinbergen is one of the two founding fathers of econometrics. The other, Ragnar Frisch, also coined the term in the sense in which it is used today. A basic tool for econometrics is the multiple linear regression model. ''Econometri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Income Inequality
There are wide varieties of economic inequality, most notably income inequality measured using the distribution of income (the amount of money people are paid) and wealth inequality measured using the distribution of wealth (the amount of wealth people own). Besides economic inequality between countries or states, there are important types of economic inequality between different groups of people. Important types of economic measurements focus on wealth, income, and consumption. There are many methods for measuring economic inequality, the Gini coefficient being a widely used one. Another type of measure is the Inequality-adjusted Human Development Index, which is a statistic composite index that takes inequality into account. Important concepts of equality include equity, equality of outcome, and equality of opportunity. Whereas globalization has reduced global inequality (between nations), it has increased inequality within nations. Income inequality between nations p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jensen's Inequality
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. Given its generality, the inequality appears in many forms depending on the context, some of which are presented below. In its simplest form the inequality states that the convex transformation of a mean is less than or equal to the mean applied after convex transformation; it is a simple corollary that the opposite is true of concave transformations. Jensen's inequality generalizes the statement that the secant line of a convex function lies ''above'' the graph of the function, which is Jensen's inequality for two points: the secant line consists of weighted means of the convex function (for ''t'' ∈ ,1, :t f(x_1) + (1-t) f(x_2), whil ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lognormal Distribution
In probability theory, a log-normal (or lognormal) distribution is a continuous probability distribution of a random variable whose logarithm is normally distributed. Thus, if the random variable is log-normally distributed, then has a normal distribution. Equivalently, if has a normal distribution, then the exponential function of , , has a log-normal distribution. A random variable which is log-normally distributed takes only positive real values. It is a convenient and useful model for measurements in exact and engineering sciences, as well as medicine, economics and other topics (e.g., energies, concentrations, lengths, prices of financial instruments, and other metrics). The distribution is occasionally referred to as the Galton distribution or Galton's distribution, after Francis Galton. The log-normal distribution has also been associated with other names, such as McAlister, Gibrat and Cobb–Douglas. A log-normal process is the statistical realization of the multipl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Generalized Entropy Index
The generalized entropy index has been proposed as a measure of income inequality in a population. It is derived from information theory as a measure of redundancy in data. In information theory a measure of redundancy can be interpreted as non-randomness or data compression; thus this interpretation also applies to this index. In addition, interpretation of biodiversity as entropy has also been proposed leading to uses of generalized entropy to quantify biodiversity. Formula The formula for general entropy for real values of \alpha is: GE(\alpha) = \begin \frac\sum_^N\left left(\frac\right)^\alpha - 1\right& \alpha \ne 0, 1,\\ \frac\sum_^N\frac\ln\frac,& \alpha=1,\\ -\frac\sum_^N\ln\frac,& \alpha=0. \end where N is the number of cases (e.g., households or families), y_i is the income for case i and \alpha is a parameter which regulates the weight given to distances between incomes at different parts of the income distribution. For large \alpha the index is especially sensit ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
United States Census Bureau
The United States Census Bureau (USCB), officially the Bureau of the Census, is a principal agency of the U.S. Federal Statistical System, responsible for producing data about the American people and economy. The Census Bureau is part of the U.S. Department of Commerce and its director is appointed by the President of the United States. The Census Bureau's primary mission is conducting the U.S. census every ten years, which allocates the seats of the U.S. House of Representatives to the states based on their population. The bureau's various censuses and surveys help allocate over $675 billion in federal funds every year and it assists states, local communities, and businesses make informed decisions. The information provided by the census informs decisions on where to build and maintain schools, hospitals, transportation infrastructure, and police and fire departments. In addition to the decennial census, the Census Bureau continually conducts over 130 surveys and p ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Descriptive Statistics
A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features from a collection of information, while descriptive statistics (in the mass noun sense) is the process of using and analysing those statistics. Descriptive statistic is distinguished from inferential statistics (or inductive statistics) by its aim to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent. This generally means that descriptive statistics, unlike inferential statistics, is not developed on the basis of probability theory, and are frequently nonparametric statistics. Even when a data analysis draws its main conclusions using inferential statistics, descriptive statistics are generally also presented. For example, in papers reporting on human subjects, typically a table is included giving the overall sample size, sample sizes in important subgroups (e.g., for each treatment o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
