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 Volume 6, Issue 1 (January 2019), Pages: 9-23


 Review Paper

 Title: Quantile mechanics: Issues arising from critical review

 Author(s): Hilary I. Okagbue 1, *, Muminu O. Adamu 2, Timothy A. Anake 1


 1Department of Mathematics, Covenant University, Canaanland, Ota, Nigeria
 2Department of Mathematics, University of Lagos, Akoka, Lagos, Nigeria

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Approximations are the alternative way of obtaining the Quantile function when the inversion method cannot be applied to distributions whose cumulative distribution functions do not have close form expressions. Approximations come in form of functional approximation, numerical algorithm, closed form expressed in terms of others and series expansions. Several quantile approximations are available which have been proven to be precise, but some issues like the presence of shape parameters, inapplicability of existing methods to complex distributions and low computational speed and accuracy place undue limitations to their effective use. Quantile mechanics (QM) is a series expansion method that addressed these issues as evidenced in the paper. Quantile mechanics is a generalization of the use of ordinary differential equations (ODE) in quantile approximation. The paper is a review that critically examined with evidences; the formulation, applications and advantages of QM over other surveyed methods. Some issues bothering on the use of QM were also discussed. The review concluded with areas of further studies which are open for scientific investigation and exploration. 

 © 2018 The Authors. Published by IASE.

 This is an open access article under the CC BY-NC-ND license (

 Keywords: Approximation, Cumulative distribution function, Probability density function, Quantile function, Quantile mechanics, Series expansion

 Article History: Received 26 June 2018, Received in revised form 27 October 2018, Accepted 27 October 2018


The comments of the reviewers were very helpful and led to an improvement of the paper. This research benefited from sponsorship from the Statistics sub-cluster of the Industrial Mathematics Research Group (TIMREG) of Covenant University and Centre for Research, Innovation and Discovery (CUCRID), Covenant University, Ota, Nigeria.

 Compliance with ethical standards

 Conflict of interest:  The authors declare that they have no conflict of interest.


 Okagbue HI, Adamu MO, and Anake TA (2019). Quantile mechanics: Issues arising from critical review. International Journal of Advanced and Applied Sciences, 6(1): 9-23

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