Statistical Modelling with Quantile Functions

By W. Gilchrist. 2000

511 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/79e79d037cbc9e39143faaa4acdacf269cbaa9b7

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

Parametric quantile regression based on the generalized gamma distribution (2013, unknown): “Approaches of this kind are nascent in the works of Gilchrist (1997, 2000, 2008).”
Quantile based entropy function in past lifetime (2013, methodology): “…various forms of lambda distributions (Ramberg and Schmeiser, 1974; Freimer et al., 1988; van Staden and Loots, 2009; Gilchrist, 2000), the power-Pareto distribution (Gilchrist, 2000, Hankin and Lee, 2006), Govindarajulu distribution (Nair et al., 2011) etc. do not have tractable distributions.”
Nonparametric Multivariate Descriptive Measures Based on Spatial Quantiles (2004, background): “In the univariate case it is equivalent to a plot of F−1(1− p)−F−1( 12) versus F−1( 12)−F−1(p), which is discussed in Gilchrist (2000).”
A Three-Parameter Asymmetric Laplace Distribution and Its Extension (2005, methodology): “We illustrate the application of ALD by fitting an asymmetric distribution of a flood data taken from the Table 1.1 of Gilchrist (2000).”
Modelling lifetimes by quantile functions using Parzen's score function (2012, methodology): “Following these, Nair and Vinesh Kumar [3] reanalysed a few data sets with the aid of model (1), the generalized lambda distribution [4] and the power-Pareto quantile function [2,5] to demonstrate the role of quantile functions in reliability studies.”
Generalized Gumbel distribution (2010, methodology): “Galton’s [6] measure of skewness ( − 1 ≤ S ≤ 1) is defined by [7], S = (upper quartile − median) + (lower quartile − median) interquartile distance .”
Probabilistic Forecasting with Spline Quantile Function RNNs (2019, background): “Probabilistic modeling with quantile functions—while not widely used in Machine Learning—has been explored in the literature for a wide range of applications (see e.g. (Gilchrist, 2000) and references therein).”
Moving Beyond the Mean in Studies of Mental Chronometry (2011, background): “Instead of plotting quantiles, one can also plot Vincentiles, which reflect the mean of a group of scores for a given individual (e.g., 1 to 10%, 11 to 20%, etc.) averaged across participants as a function of condition (Gilchrist, 2000).”
Asymptotically exact inference in differentiable generative models (2016, background): “Although these quantile distributions can offer very flexible descriptions of shape of a distribution [36] often the quantile function will not have a closed-form inverse meaning their CDF and so density function cannot be evaluated analytically.”
The alchemy of probability distributions: beyond Gram-Charlier expansions, and a skew-kurtotic-normal distribution from a rank transmutation map (2009, methodology): “nk transmutation maps (RTMs) v = G[F−1(u)], where F and G are cumulative distribution functions (CDFs). Such maps have attracted the attention of statisticians in the past, in particular of Gilchrist [11], who refers to STMs and RTMs as Q-transformations and P-transformations, respectively. In this ”
Theory and Applications of the Unit Gamma/Gompertz Distribution (2021, background): “The book of [17] contains more material on the issue of quantile analysis.”
Quantile based entropy function (2012, methodology): “…forms of lambda distributions (Ramberg and Schmeiser, 1974; Freimer et al., 1998; Gilchrist, 2000; van Staden and Loots, 2009), the power-Pareto distribution (Gilchrist, 2000; Hankin and Lee, 2006), Govindarajulu distribution (Nair et al., 2011) etc. do not have tractable distribution functions.”
On Families of Distributions with Shape Parameters (2015, unknown): “Other prominent references include Fern´andez & Steel (1998), Mudholkar & Hutson (2000) and Arellano-Valle, G´omez & Quintana (2005).”