CDF‐quantile distributions for modelling random variables on the unit interval. (17th March 2017)

• Record Type: Journal Article
• Authors: Smithson, Michael; Shou, Yiyun
• Is Part Of: British journal of mathematical & statistical psychology. Volume 70:Part 3(2017:Nov.)
• Page Start: 412
• Page End: 438
• Publication Date: 2017-03-17
• Subjects: density estimation -- quantile regression -- quantile function -- unit interval; Psychometrics -- Periodicals; Psychology -- Mathematical models -- Periodicals; Psychology -- Statistical methods -- Periodicals; 150.727
• DOI: 10.1111/bmsp.12091
• Languages: English
• ISSNs: 0007-1102

Abstract

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.