Journal
BRITISH JOURNAL OF MATHEMATICAL & STATISTICAL PSYCHOLOGY
Volume 70, Issue 3, Pages 412-438Publisher
WILEY
DOI: 10.1111/bmsp.12091
Keywords
density estimation; quantile regression; quantile function; unit interval
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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.
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