Quantile Approximation of the Chi–square Distribution using the Quantile Mechanics
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Abstract
Description
In the field of probability and statistics, the
quantile function and the quantile density function which is the
derivative of the quantile function are one of the important
ways of characterizing probability distributions and as well,
can serve as a viable alternative to the probability mass
function or probability density function. The quantile function
(QF) and the cumulative distribution function (CDF) of the
chi-square distribution do not have closed form
representations except at degrees of freedom equals to two and
as such researchers devise some methods for their
approximations. One of the available methods is the quantile
mechanics approach. The paper is focused on using the
quantile mechanics approach to obtain the quantile density
function and their corresponding quartiles or percentage
points. The outcome of the method is second order nonlinear
ordinary differential equation (ODE) which was solved using
the traditional power series method. The quantile density
function was transformed to obtain the respective percentage
points (quartiles) which were represented on a table. The
results compared favorably with known results at high
quartiles. A very clear application of this method will help in
modeling and simulation of physical processes.
Keywords
Q Science (General), QA Mathematics