Solutions of Chi-square Quantile Differential Equation
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The quantile function of probability distributions
is often sought after because of their usefulness. The quantile
function of some distributions cannot be easily obtained by
inversion method and approximation is the only alternative
way. Several ways of quantile approximation are available, of
which quantile mechanics is one of such approach. This paper
is focused on the use of quantile mechanics approach to obtain
the quantile ordinary differential equation of the Chi-square
distribution since the quantile function of the distribution does
not have close form representations except at degrees of
freedom equals to two. Power series, Adomian decomposition
method (ADM) and differential transform method (DTM) was
used to find the solution of the nonlinear Chi-square quantile
differential equation at degrees of freedom equals to two. The
approximate solutions converge to the closed (exact) solution.
Furthermore, power series method was used to obtain the
solutions for other degrees of freedom and series expansion
was obtained for large degrees of freedom.
Keywords
Q Science (General), QA Mathematics