| dbo:abstract |
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. The family of Pareto distributions is parameterized by * a positive number κ that is the smallest value that a random variable with a Pareto distribution can take. As applied to distribution of incomes, κ is the lowest income of any person in the population; and * a positive number θ the "Pareto index"; as this increases, the tail of the distribution gets thinner. As applied to distribution of incomes, this means that the larger the value of the Pareto index θ the smaller the proportion of incomes many times as big as the smallest incomes. 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. For example, it may be observed that 45% of individuals in the sample have incomes below a = 35,000peryear,and5535,000 per year, and 55% have incomes below b = 35,000peryear,and5540,000 per year. Let Pa = proportion of the sample that lies below a;Pb = proportion of the sample that lies below b. Then the estimates of κ and θ are and The estimate of the median would then be since the actual population median is (en) 帕累托插值法（Pareto interpolation）是寻找一组数据的中位数的非线性插值方法,，常被用于经济学中分析收入。该方法假设数据符合被称为帕累托分布的曲线。 中位数由下面公式给出： 其中参数κ和θ由下列公式给出： 且 其中 a = 包含中数的分类的下限b = 包含中数的分类的上限Pa = 分布的低于（lies below）下限的部分Pb = 分布的低于（lies below）上限的部分 (zh) |
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http://mumford.albany.edu/census/CityProfiles/Profiles/MHHINote.htm https://web.archive.org/web/20060825221627/http:/www.sipp.census.gov/sipp/sourceac/S%26A01_20060323_Long%28S%26A-3%29.pdf |
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owl:Thing |
| rdfs:comment |
帕累托插值法（Pareto interpolation）是寻找一组数据的中位数的非线性插值方法,，常被用于经济学中分析收入。该方法假设数据符合被称为帕累托分布的曲线。 中位数由下面公式给出： 其中参数κ和θ由下列公式给出： 且 其中 a = 包含中数的分类的下限b = 包含中数的分类的上限Pa = 分布的低于（lies below）下限的部分Pb = 分布的低于（lies below）上限的部分 (zh) 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. The family of Pareto distributions is parameterized by Let Pa = proportion of the sample that lies below a;Pb = proportion of the sample that lies below b. Then the estimates of κ and θ are and The estimate of the median would then be since the actual population median is (en) |
| rdfs:label |
Pareto interpolation (en) 帕累托插值 (zh) |
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