Smithson Michael, Shou Yiyun
The Australian National University, Canberra, Australian Capital Territory, Australia.
Br J Math Stat Psychol. 2017 Nov;70(3):412-438. doi: 10.1111/bmsp.12091. Epub 2017 Mar 17.
This paper introduces a two-parameter family of distributions for modelling random variables on the (0,1) interval by applying the cumulative distribution function of one 'parent' distribution to the quantile function of another. Family members have explicit probability density functions, cumulative distribution functions and quantiles in a location parameter and a dispersion parameter. They capture a wide variety of shapes that the beta and Kumaraswamy distributions cannot. They are amenable to likelihood inference, and enable a wide variety of quantile regression models, with predictors for both the location and dispersion parameters. We demonstrate their applicability to psychological research problems and their utility in modelling real data.
本文介绍了一个双参数分布族，该分布族通过将一个“母”分布的累积分布函数应用于另一个分布的分位数函数，对(0,1)区间上的随机变量进行建模。族成员在位置参数和离散参数方面具有明确的概率密度函数、累积分布函数和分位数。它们捕捉了贝塔分布和库马尔斯瓦米分布所不能捕捉的多种形状。它们适用于似然推断，并能实现多种分位数回归模型，同时具有位置参数和离散参数的预测变量。我们展示了它们在心理学研究问题中的适用性以及在对实际数据建模中的效用。
