Quantile Statistics Overlay

Statistical modeling with Quantile Functions

Quantile Statistics Overlay highlights important contributions in the field of data analysis using quantile functions. The journal is established to expand and further the research area pioneered by Emmanuel Parzen (1929–2016) and Warren G. Gilchrist (1932–2015).

Superquantile function of order n and their applications in reliability and entropy (2025)

N. Unnikrishnan Nair, S.M. Sunoj, Silpa Subhash

https://doi.org/10.1016/j.spl.2025.110457

May 30, 2025 - New and exciting direction for quantile function research . Excellent extension connecting to the concept of mean life function

A quantile-based bivariate distribution (2025)

Shifna P R, N. Unnikrishnan Nair, S. M. Sunoj

http://arxiv.org/abs/2503.11289v1

Mar 25, 2025 - Bivariate distribution defined by a bivariate quantile function

The Relative Information Generating Function-A Quantile Approach (2024)

Sankaran P. G., Sunoj S. M., Pavithra Hariharan

http://arxiv.org/abs/2412.02253v1

Dec 07, 2024 - Generalization of quantile KL divergence

Bayesian estimation of a quantile-based factor model (2024)

Edoardo Redivo, Cinzia Viroli

http://dx.doi.org/10.1080/00949655.2024.2406092

Sep 25, 2024 - Extension of quantile-based inference into the factor models

Quantile-based information generating functions and their properties and uses (2024)

Suchandan Kayal, N. Balakrishnan

http://dx.doi.org/10.1017/s0269964824000068

May 28, 2024

Quantile-based cumulative Kullback-Leibler divergence in past lifetime: Some properties and applications (2024)

S.M. Sunoj, P. Saranya

http://dx.doi.org/10.1080/03610926.2024.2352016

May 17, 2024 - Further development of QKL

Additive hazards quantile model (2023)

N. Unnikrishnan Nair, S. M. Sunoj, Namitha Suresh

http://dx.doi.org/10.1007/s00184-023-00924-2

Sep 14, 2023 - Excellent extension of modeling based on the hazard quantile functions

Analysis and Applications of Quantile Approach on Residual Extropy (2023)

Amir Hamzeh Khammar, Vahideh Ahrari, Seyed Mahdi Amir Jahanshahi

http://dx.doi.org/10.19139/soic-2310-5070-1226

Sep 06, 2023 - Extropy in quantile framework

Quantile based Tsallis entropy in residual lifetime (2018)

A.H. Khammar, S.M.A. Jahanshahi

http://dx.doi.org/10.1016/j.physa.2017.11.030

Sep 06, 2023 - Quantile version of Tsallis entropy

Some New Results on Renyi Entropy and Its Relative Measure (2022)

N. Unnikrishnan Nair, S. M. Sunoj, Rajesh G.

http://dx.doi.org/10.1177/00080683221137197

Sep 06, 2023 - Development of Renyi Entropy in the quantile framework

Quantile based entropy function (2012)

S.M. Sunoj, P.G. Sankaran

http://dx.doi.org/10.1016/j.spl.2012.02.005

Sep 06, 2023 - A quantile-based version of entropy underlying KL divergence and other measures. Fundamental paper for comparing quantile functions

The tenets of quantile-based inference in Bayesian models (2023)

Dmytro Perepolkin, Benjamin Goodrich, Ullrika Sahlin

http://dx.doi.org/10.1016/j.csda.2023.107795

Jun 12, 2023 - This article builds on the ideas of Gilchrist (2000), Rayner and MacGillivray (2002), Nair et al. (2020) and systematically presents and illustrates the Bayesian inference using quantile functions.

Mixture Quantiles Estimated by Constrained Linear Regression (2023)

Cheng Peng, Yizhou Li, Stan Uryasev

http://arxiv.org/abs/2305.00081v1

Jun 06, 2023 - Excellent demonstration of the versatility of Gilchrist combinations. The constrained optimization algorithm ensures that the component weights stay positive. The proposed estimator is asymptotically q-Wasserstein distance.

Statistical Modeling Based on Quantile Distribution Functions (2010)

Warren Gilchrist

http://dx.doi.org/10.1201/b10159-16

Mar 02, 2023 - Last paper by Gilchrist. Compendium of all of the things he worked on during his career. Lots of tables and materials to dig through.

Kullback–Leibler divergence: A quantile approach (2016)

P.G. Sankaran, S.M. Sunoj, N. Unnikrishnan Nair

http://dx.doi.org/10.1016/j.spl.2016.01.007

Mar 02, 2023 - The quantile-based approach to comparing distributions.

The shapes of things to come: probability density quantiles (2017)

Robert G. Staudte

http://dx.doi.org/10.1080/02331888.2016.1277225

Mar 02, 2023 - A compact way to compare distributions on unit square. A very promising approach, which remains under-appreciated.

Properties of Bivariate Distributions Represented through Quantile Functions (2023)

N. Unnikrishnan Nair, B. Vineshkumar

http://dx.doi.org/10.1080/01966324.2021.2016522

Feb 27, 2023 - The foundational paper for representing bivariate distributions with quantile functions.

Bayesian inference in quantile functions (2022)

N. Unnikrishnan Nair, P. G. Sankaran, M. Dileepkumar

http://dx.doi.org/10.1080/03610926.2020.1827430

Feb 27, 2023 - One of the most important papers connecting Quantile statistics to Bayesian analysis via the quantile likelihood and prior.

Quantile Probability and Statistical Data Modeling (2004)

Emanuel Parzen

http://dx.doi.org/10.1214/088342304000000387

Feb 27, 2023 - One of the best articles summarizing Parzen's contribution to Quantile Statistics. Includes discussion of comparison distribution function and its Bayesian application.

Quantile cumulative distribution function and its applications (2023)

Angel Mathew

http://dx.doi.org/10.1080/03610926.2023.2176716

Feb 27, 2023 - The author revisits and explores the innovative method of comparing the distributions proposed by Emmanuel Parzen (1982).

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