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Solutions of Chi-square Quantile Differential Equation

Okagbue, H. I. and Adamu, M. O. and Anake, T. A. (2017) Solutions of Chi-square Quantile Differential Equation. In: World Congress on Engineering and Computer Science, October 25-27, 2017, San Francisco, USA.

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Abstract

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.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Chi-square, quantile function, differential equation, shape parameter, Adomian decomposition method, differential transform method.
Subjects: Q Science > Q Science (General)
Q Science > QA Mathematics
Divisions: Faculty of Engineering, Science and Mathematics > School of Mathematics
Depositing User: Mrs Hannah Akinwumi
Date Deposited: 17 Nov 2017 08:07
Last Modified: 17 Nov 2017 08:07
URI: http://eprints.covenantuniversity.edu.ng/id/eprint/9681

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