title: CDF-quantile distributions for modelling random variables on the unit interval.
abstract: 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.
authors.affiliation: The Australian National University, Canberra, Australian Capital Territory, Australia.
authors.forename: Michael
authors.initials: M
authors.lastname: Smithson
authors.affiliation: The Australian National University, Canberra, Australian Capital Territory, Australia.
authors.forename: Yiyun
authors.initials: Y
authors.lastname: Shou
mesh_terms: D003198:Computer Simulation; D006801:Humans; D016013:Likelihood Functions; D016015:Logistic Models; D015233:Models, Statistical; D011336:Probability; D011584:Psychology / Q000706:statistics & numerical data; D012044:Regression Analysis
keywords: density estimation; quantile function; quantile regression; unit interval