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Topic: Pareto interpolation

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In the News (Tue 25 Jun 19)

  Pareto interpolation - Wikipedia, the free encyclopedia
Pareto interpolation is a method of estimating the median and other properties of a population that follows a Pareto distribution.
It is used in economics when analysing the distribution of incomes in a population, when one must base estimates on a relatively small random sample taken from the population.
Pareto interpolation can be used when the available information includes the proportion of the sample that falls below each of two specified numbers a < b.
en.wikipedia.org /wiki/Pareto_interpolation   (288 words)

 Pareto distribution
The Pareto distribution named after the Italian economist Vilfredo Pareto is a power law distribution found in a large number of real-world situations.
If X is a random variable with a Pareto distribution, then the probability distribution of X is characterized by the statement
If the value of k is chosen judiciously then the Pareto distribution obeys the "80-20 rule".
www.ebroadcast.com.au /lookup/encyclopedia/pa/Pareto_distribution.html   (179 words)

 Reference.com/Encyclopedia/Pareto distribution
Pareto originally used this distribution to describe the allocation of wealth among individuals since it seemed to show rather well the way that a larger portion of the wealth of any society is owned by a smaller percentage of the people in that society.
This idea is sometimes expressed more simply as the Pareto principle or the "80-20 rule" which says that 20% of the population owns 80% of the wealth.
One can easily generate a random sample from Pareto distribution by mixing two random variables, which are usually built-in in many statistical tools.
www.reference.com /browse/wiki/Pareto_distribution   (976 words)

 Derived Measures from STF3 APPENDIX B, "Definitions of Subject Characteristics"
Interpolation frequently is used in calculating medians or quartiles based on interval data and in approximating standard errors from tables.
Linear interpolation is used to estimate values of a function between two known values.
In Pareto interpolation, the median is derived by interpolating between the logarithms of the upper and lower income limits of the median category.
www.census.gov /geo/lv4help/apen_bderive.html   (551 words)

 Description for median household income calculation   (Site not responding. Last check: 2007-10-14)
When it is necessary to aggregate central cities, suburbs, or portions of a metropolitan area from different states, we follow the methods of interpolation used by the Census Bureau based on grouped income data.
Linear interpolation is described in most textbooks on statistical methods, so we will not discuss it further.
However, because pareto interpolation is less well-covered, we provide a brief description of the method.
mumford1.dyndns.org /cen2000/CityProfiles/Profiles/MHHINote.htm   (400 words)

 [CTPP] Pareto Interpolation   (Site not responding. Last check: 2007-10-14)
I confirmed that the difference between the Pareto figures and the Census figures are most likely due to the fact that the Census Bureau calculates median value based upon more detailed distribution information than it releases to the public.
Notice that the Pareto calculations are sometimes higher and lower than the official figures, but the linear calculations are higher.
Most likely this observation is because Pareto uses a logarithmic curve rather than a straight line.
www.chrispy.net /pipermail/ctpp-news/2002-June/000538.html   (312 words)

 DAKOTA: Strategy Commands
The surrogate model can be a global data fit (e.g., regression or interpolation of data generated from a design of computer experiments), a multipoint approximation, a local Taylor Series expansion, or a model hierarchy approximation (e.g., a low-fidelity simulation model), whereas the truth model involves a high-fidelity simulation model.
A trust region strategy is used to manage the optimization process to maintain acceptable accuracy between the surrogate model and the truth model (by limiting the range over which the surrogate model is trusted).
This set of optimal solutions defines a "Pareto set," which is useful for investigating design trade-offs between competing objectives.
www.cs.sandia.gov /DAKOTA/licensing/release/html-ref/StratCommands.html   (1999 words)

 Assessing Reliability of SIPP / Sampling Error
Since the median is greater than $200, Pareto interpolation is indicated.
Thus, the 68percent confidence interval on the estimated median is from $2,091 to $2,154.
For this report, we recommend Pareto interpolation for any point in a monthly income interval greater than $200, and linear interpolation otherwise.
www.sipp.census.gov /sipp/chap7-1.htm   (3610 words)

 Róbinson Rojas.- United States: Income Inequality. A BRIEF LOOK AT POSTWAR U.S. INCOME INEQUALITY, by Daniel H. ...   (Site not responding. Last check: 2007-10-14)
12/ These estimates were derived using pareto interpolation and may differ from published data which were derived using linear interpolation.
Prior to this year all medians were derived using linear interpolation.
5/ These estimates were derived using pareto interpolation and may differ from published data which were derived using linear interpolation.
www.rrojasdatabank.org /incus1.htm   (2556 words)

 Journey to Work: Florida Edition: Definitions
Median income figures are calculated using linear interpolation if the width of the interval containing the estimate is $2,500 or less.
If the width of the interval containing the estimate is greater than $2,500, Pareto interpolation is used.
This question was asked of people who indicated that they worked at some time during the reference week and who reported that they worked outside their home.
www.j2w.usf.edu /definitions.asp   (1508 words)

 99 Workforce Development : Glossary
Pareto interpolation is used if the median falls in any income intervals with a width of $5,000 or more, except for the lowest income interval.
For income intervals with a width of $2,500 and the lowest interval, <$5,000, linear interpolation is used.
Metropolitan Statistical Area A large population nucleus (a county or group of counties with a total population of at least 75,000 and a central city or urbanized area of at least 50,000) together with adjacent communities that have a high degree of social and economic integration within that nucleus.
www.caction.org /IssueAreas/Workforce/1999Assessment/GLOSSARY.html   (954 words)

 Source and Accuracy Statement for the 1992 Panel 7-Wave Longitudinal File
The most common are simple linear interpolation and Pareto interpolation.
Implementing Pareto interpolation, the upper bound of a 68-percent confidence interval for the median is
If linear interpolation is used, the median is estimated using formula (13) to be $18,441 and the 68-percent confidence interval of the estimated median is from $18,338 to $18,544.
www.bls.census.gov /sipp/sourceac/sourceac_1.htm   (8404 words)

 Data on Income (US Census)
Median household or family income figures of $50,000 or less are calculated using linear interpolation.
All other median income amounts are derived through Pareto interpolation.
Mean Income--This is the amount obtained by dividing the total income of a particular statistical universe by the number of units in that universe.
www.sliceanddicedata.com /detfil8.htm   (2546 words)

 Pareto distribution - Wikipedia, the free encyclopedia
The Pareto distribution, named after the Italian economist Vilfredo Pareto, is a power law probability distribution that coincides with social, scientific, geophysical, and many other types of observable phenomena.
[edit] Generating a random sample from Pareto distribution
Pareto • Pearson • polar • raised cosine • Rayleigh • relativistic Breit-Wigner • Rice • Student's t • triangular • type-1 Gumbel • type-2 Gumbel • uniform • Voigt • von Mises • Weibull • Wigner semicircle • Wilks' lambda
en.wikipedia.org /wiki/Pareto_distribution   (1108 words)

 Chicago Community Area Health And Demographic Data   (Site not responding. Last check: 2007-10-14)
This technique is commonly known as Linear Interpolation.
The program also adjusts median incomes lower than $10,000 and higher than $50,000, based on the assumption that incomes beyond these extremes are not linearly distributed.
The Pareto Interpolation that was used to calculate these latter medians is also used by the Census Bureau in similar circumstances.
www.chas.uchicago.edu /healthdata/atlas/intro.html   (1517 words)

 Changes in Methodology for the March Current Population Survey
These estimates were derived using Pareto interpolation and may differ from published data which were derived using linear interpolation.
First year medians are derived using both Pareto and linear interpolation.
Also starting in 1999, when looking at the quintiles in the historical income series, you will notice that the 50th percentile is based on micro-sorted data and may differ from the median published in the income report which is based on linearly interpolated grouped data.
www.census.gov /hhes/www/income/histinc/hstchg.html   (561 words)

 census data characteristics of population and housing from research demographics   (Site not responding. Last check: 2007-10-14)
Median earnings is restricted to individuals 16 years old and over and is computed on the basis of a standard distribution.
Median earnings figures are calculated using linear interpolation if the width of the interval containing the estimate is $2,500 or less.
Aggregate earnings are the sum of wage/salary and net self-employment income for a particular universe of people 16 years old and over.
www.researchdemographics.com /data_characteristics.htm   (8953 words)

 [CTPP] Pareto Interpolation   (Site not responding. Last check: 2007-10-14)
It also means we can't calculate standard errors for medians.
I calculated the median income for Cook County from the GDP using Pareto and it is about $500 different than the Bureau's number.
Jim Bash On Tue, 18 Jun 2002, Daryl Scott wrote: > I am trying to calculate the median income for a region using the Pareto Interpolation method like the Census Bureau.
www.chrispy.net /pipermail/ctpp-news/2002-June/000536.html   (383 words)

 2000 Census Data
For suburbs, for cities where there is more than one central city in the metropolis, and for metro areas that cross state lines, we provide estimates of the median income.
These are based on a Pareto curve interpolation from grouped data.
For 1990, where income has been reported in 25 categories, the estimates are quite precise.
www.albany.edu /mumford/census/cities/tnotes.htm   (713 words)

 Online Spin » Blog Archive » The Big Hump
Before the Long Tail (a wonderful, well-written article by Chris Anderson that appeared in Wired magazine a while back), there was the Italian economist, Vilfredo Pareto, who created a mathematical formula in 1906 to describe the unequal distribution of wealth in his country.
One also must describe and factor in the Kalman filters into the Zipf-Mandelbrot law and Pareto interpolation to accurately determine the level of bias in the sample set.
For example, if one were raised with a vocabulary devoid of S and T words, the curves would look markedly different from a full vocabulary.
blogs.mediapost.com /spin/?p=569   (1751 words)

 "Dependency Theory: An Introduction," Vincent Ferraro, Mount Holyoke College, July 1966
Indeed, their studies suggested that economic activity in the richer countries often led to serious economic problems in the poorer countries.
Such a possibility was not predicted by neoclassical theory, which had assumed that economic growth was beneficial to all (Pareto optimal) even if the benefits were not always equally shared.
Prebisch's initial explanation for the phenomenon was very straightforward: poor countries exported primary commodities to the rich countries who then manufactured products out of those commodities and sold them back to the poorer countries.
www.mtholyoke.edu /acad/intrel/depend.htm   (2751 words)

 CenterSpace - NMath Core, C# Math Library, BLAS, .NET Numerical Libraries, C#, csharp, VB.NET
LU factorization for a matrix, as well as functions for solving linear systems, computing determinants, inverses, and condition numbers.
Random number generation from various probability distributions, including the uniform, triangular, normal, Poisson, gamma, binomial, exponential, Pareto, and log normal distributions.
Polynomial encapsulation, interpolation, and exact differentiation and integration.
www.centerspace.net /products.php?page=1   (203 words)

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