Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution
Smooth centile curves for skew and kurtotic data modelled using the Box-Cox power exponential distribution
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DOI：
10.1002/sim.1861
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发表时间：
2004-10-15
影响因子：
2
通讯作者：
Stasinopoulos, DM
中科院分区：
文献类型：
--
作者：
Rigby, RA;Stasinopoulos, DM
本文提出的Box-Cox幂指数（BCPE）分布为因变量Y提供了一个模型，该分布同时表现出偏度和峰度（leptokurtosis或platykurtosis）。该分布由幂变换Y-nu定义，该幂变换具有带参数τ的移位和缩放（截断）标准幂指数分布。该分布具有四个参数，并表示为BCPE（mu，sigma，nu，tau）。参数mu、sigma、nu和tau可以分别解释为与位置（中位数）、尺度（近似变异系数）、偏度（对称性转换）和峰度（幂指数参数）相关。通过将分布的四个参数中的每一个建模为解释变量的平滑非参数函数，获得平滑百分位数曲线。Fisher评分算法用于通过最大化惩罚似然来拟合非参数模型。第一和预期的第二和交叉导数的可能性，相对于μ，西格玛，努和τ，所需的算法，提供。BCPE分布的百分位数易于计算，非常适合于百分位数估计，本文将BCPE分布应用于平滑百分位数估计，将LMS百分位数估计方法推广到峰度（以及偏度）不同于正态分布的数据，称为LMSP百分位数估计方法。百分位数估计的LMSP方法适用于荷兰男性对年龄的体重指数建模。版权所有0 2004年约翰威利父子有限公司。
The Box-Cox power exponential (BCPE) distribution, developed in this paper, provides a model for a dependent variable Y exhibiting both skewness and kurtosis (leptokurtosis or platykurtosis). The distribution is defined by a power transformation Y-nu having a shifted and scaled (truncated) standard power exponential distribution with parameter tau. The distribution has four parameters and is denoted BCPE(mu, sigma, nu, tau). The parameters, mu, sigma, nu and tau, may be interpreted as relating to location (median), scale (approximate coefficient of variation), skewness (transfort-nation to symmetry) and kurtosis (power exponential parameter), respectively. Smooth centile curves are obtained by modelling each of the four parameters of the distribution as a smooth non-parametric function of an explanatory variable. A Fisher scoring algorithm is used to fit the non-parametric model by maximizing a penalized likelihood. The first and expected second and cross derivatives of the likelihood, with respect to mu, sigma, nu and tau, required for the algorithm, are provided. The centiles of the BCPE distribution are easy to calculate, so it is highly suited to centile estimation.This application of the BCPE distribution to smooth centile estimation provides a generalization of the LMS method of the centile estimation to data exhibiting kurtosis (as well as skewness) different from that of a normal distribution and is named here the LMSP method of centile estimation. The LMSP method of centile estimation is applied to modelling the body mass index of Dutch males against age. Copyright 0 2004 John Wiley Sons, Ltd.