A Note on Generalized Inverses of Distribution Function and Quantile Transformation

Changyong Feng, Hongyue Wang, Xin Tu, Jeanne Kowalski

Type: Article

Publication Date: 2012-01-01

Citations: 13

DOI: https://doi.org/10.4236/am.2012.312a289

Abstract

In this paper we study the relations of four possible generalized inverses of a general distribution functions and their right-continuity properties. We correct a right-continuity result of the generalized inverse used in statistical literature. We also prove the validity of a new generalized inverse which is always right-continuous.

Locations

Applied Mathematics - View - PDF

Similar Works

Action	Title	Year	Authors
+ PDF Chat	A New Generalization of the Inverse Distributions: Properties and Applications	2020	Clement Boateng Ampadu
+	A New Generalized Burr Family of Distributions Based on Quantile Function	2017	Arslan Nasir Mohammad Al‐Jarrah Farrukh Jamal M. H. Tahir
+	A type of 'inverseness' of certain distributions and the inverse normal distribution	1978	Stanley Nkhensani Tlakula
+	Some properties and applications of a distribution-free quantile estimator	2016	Robert Wieczorkowski Ryszard Zieliński
+	A Generalized Quantile Estimator under Censoring.	1987	Yuhlong Lio W. J. Padgett
+	Functional data analysis of generalized regression quantiles	2013	Mengmeng Guo Lan Zhou Jianhua Z. Huang Wolfgang Karl Härdle
+	A class of distributions with the linear mean residual quantile function and it’s generalizations	2013	N.N. Midhu P. G. Sankaran N. Unnikrishnan Nair
+ PDF Chat	A new reduced quantile function for generating families of distributions	2024	Chukwuma Prince O Harrison Etaga O Ibeakuzie Precious Anabike Ifeanyi C Obulezi Okechukwu J
+	A new quantile regression model for bounded responses with applications	2025	Patrícia Stülp Jorge L. Bazán Luis Hilmar Valdivieso Serrano
+ PDF Chat	Truncated Inverse Generalized Rayleigh Distribution and Some Properties	2023	Bayda Atiya Kalaf Noor Abdul Ameer Jabar Umar Yusuf Madaki
+	Properties of Transformation Quantile Regression Model	2013	Grażyna Trzpiot
+	Estimation of quantile density function based on regression quantiles	1995	Yadolah Dodge Jana Jurečková
+	Quantile dependence: A generalization of upper and lower tail dependence	2024	Ali Dastbaravarde Ali Dolati
+	A new family of quantile functions and its applications	2020	Dileep Kumar Maladan P. G. Sankaran
+	Estimation Method for Quantile Regression	2009	Grażyna Trzpiot
+ PDF Chat	On generalized classes of exponential distribution using T-X family framework	2018	Muhammad Zubair Ayman Alzaatreh Gauss M. Cordeiro M. H. Tahir Muhammad Mansoor
+ PDF Chat	Quantile regression based on the skewed exponential power distribution	2023	Lukas Arnroth Johan Vegelius
+ PDF Chat	On the Extended Generalized Inverse Exponential Distribution with Its Applications	2020	Sule Ibrahim Bello Olalekan Akanji Lawal Hammed Olanrewaju
+	On discrete generalization of the inverse exponential distribution: Properties, characterizations and applications	2023	Hanan Haj Ahmad Ehab M. Almetwally
+	A Useful Extension of the Inverse Exponential Distribution	2018	Pelumi E. Oguntunde A. O. Adejumo Mundher A. Khaleel E. A. Owoloko Hilary I. Okagbue A. A. Opanuga

Works That Cite This (9)

Action	Title	Year	Authors
+ PDF Chat	A Bayesian Approach to Multiple-Output Quantile Regression	2022	Michael Guggisberg
+ PDF Chat	On possibilistic representations of fuzzy intervals	2017	Luciano Stefanini Maria Letizia Guerra
+ PDF Chat	An analysis of the Rüschendorf transform - with a view towards Sklar’s Theorem	2015	Frank Oertel
+ PDF Chat	On semi-continuity and continuity of the smallest and largest minimizing point of real convex functions with applications in probability and statistics	2023	Dietmar Ferger
+	An uncertain minimization problem: robust optimization versus optimization of robustness	2022	Moussa Barro Sado Traoré
+	Orlicz spaces equipped with s-norms	2019	Marek Wisła
+	Solving the Iterative Differential Equation $$-\gamma g' = g^{-1}$$	2023	Roland Miyamoto J. Sander
+	Asymptotically Quasi-inverse Functions	2018	Valeriĭ V. Buldygin Karl‐Heinz Indlekofer Oleg Klesov Josef Steinebach
+	Brownian Motions on Star Graphs with Non-Local Boundary Conditions	2018	Florian Werner

Works Cited by This (5)

Action	Title	Year	Authors
+	Probability: Theory and Examples.	1992	Kathryn Prewitt Richard Durrett
+ PDF Chat	Statistical Models Based on Counting Processes	1997	Xavier Bry Per Kragh Andersen Ørnulf Borgan Richard D. Gill Niels Keiding Ørnulf Borgan
+ PDF Chat	Quartiles in Elementary Statistics	2006	Eric Langford
+	Statistical Models Based on Counting Processes	1993	Per Kragh Andersen Ørnulf Borgan Richard D. Gill Niels Keiding
+	Probability and measure theory	1999	R. Ash Catherine Doléans-Dade