CLOSED FORM EXPRESSION OF THE QUANTILE FUNCTION OF MAXWELL-BOLTZMANN DISTRIBUTION
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The closed form expression for the quantile function of some distributions is
not available because of the intractable nature of the cumulative
distribution function and as such inversion method cannot be applied to
obtain the quantile function. This paper reports the development of the
closed form expressions of the inverse cumulative distribution (quantile)
function of Maxwell-Boltzmann distribution by the hybrid combination of
quantile mechanics and cubic spline interpolation. The estimated closed
form expressions obtained are close to the reference values (R software
values) up to an average of 8 decimal places. The result can be adapted
and implemented using any mathematical software. The implementation of
the results of this paper can create insight into a better use of Maxwell-
Boltzmann distribution in statistical mechanics. Now the closed form
expression of the quantile function is available to be used in simulation of
physical systems described by the distribution. This will change the way
and manner physical systems fitted with the Maxwell-Boltzmann
distribution are modeled especially in the tail area of the distribution.
Furthermore, the parameters can be parameterized to simulate thermal
velocity effects.
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QA Mathematics