Quantile mechanics: Issues arising from critical review
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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.
Keywords
QA Mathematics