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Quantile Approximation of the Chi–square Distribution using the Quantile Mechanics

Okagbue, H. I. and Adamu, M. O. and Anake, T. A. (2017) Quantile Approximation of the Chi–square Distribution using the Quantile Mechanics. In: World Congress on Engineering and Computer Science, October 25-27, 2017, San Francisco, USA.

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Abstract

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.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: Quantile, Quantile density function, Quantile mechanics, percentage points, Chi-square, approximation.
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: 16 Nov 2017 07:32
Last Modified: 16 Nov 2017 07:32
URI: http://eprints.covenantuniversity.edu.ng/id/eprint/9668

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