κ-Generalized statistics in personal income distribution
κ-Generalized statistics in personal income distribution
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DOI：
10.1140/epjb/e2007-00120-9
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发表时间：
2007-05-01
影响因子：
1.6
通讯作者：
Kaniadakis, G.
中科院分区：
文献类型：
--
作者：
Clementi, F.;Gallegati, M.;Kaniadakis, G.
从文献[G]中提出的广义指数函数exp(k)(x) =(根1 + k(2)x(2) + kx)（1/k）出发，exp(0) (x) = exp(x)。为了分析德国、意大利和英国的个人收入分配数据，我们考虑了生存函数P- b> (x) = expk (-beta(alpha)(x))，其中x是R+、alpha、beta > 0的一个元素，k是[0,1]的一个元素。上述定义的分布是拉伸指数函数P->(0) (x)=exp(k) （-beta x(alpha)）的连续单参数变形-当kappa接近零时，其在x - >0和x ->无限区域的表现方式非常不同。它的体积非常接近拉伸的指数型，而它的尾部则按照幂律P->(x)衰减，类似于（2 beta kappa）（-1/kappa） x（-alpha/kappa）。这使得kappa广义函数特别适合同时描述最富裕部分和绝大多数人口之间的收入分配，通常拟合不同的曲线。在整个范围内，我们的理论模型与个人收入的观测数据非常吻合。
Starting from the generalized exponential function exp(k)(x) = (root 1 + k(2)x(2) + kx)(1/k), with exp(0) (x) = exp(x), proposed in reference [G. Kaniadakis, Physica A 296, 405 ( 2001)], the survival function P-> (x) = expk (-beta(alpha)(x)), where x is an element of R+, alpha, beta > 0, and k is an element of [0,1), is considered in order to analyze the data on personal income distribution for Germany, Italy, and the United Kingdom. The above defined distribution is a continuous one-parameter deformation of the stretched exponential function P->(0) (x)=exp(k) (-beta x(alpha)) - to which reduces as kappa approaches zero behaving in very different way in the x -> 0 and x -> infinity regions. Its bulk is very close to the stretched exponential one, whereas its tail decays following the power-law P->(x)similar to(2 beta kappa)(-1/kappa) x(-alpha/kappa). This makes the kappa-generalized function particularly suitable to describe simultaneously the income distribution among both the richest part and the vast majority of the population, generally fitting different curves. An excellent agreement is found between our theoretical model and the observational data on personal income over their entire range.